Chapter 3 Review and Practice Test

Learning objectives

Learning objectives

• Review the key ideas of this chapter.

• Apply the chapter's methods to review exercises.

• Check your understanding with a practice test.

##

Worked example

boundary line

domain of a relation

x

function

A function is a relation that assigns to each element in its domain exactly one element in the range.

horizontal line

y

intercepts of a line

x

y

linear equation

A

B

linear inequality

A

B

mapping

A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.

ordered pair

x

y

origin

x

y

parallel lines

Parallel lines are lines in the same plane that do not intersect.

perpendicular lines

Perpendicular lines are lines in the same plane that form a right angle.

point-slope form

m

range of a relation

y-

relation

x

y

solution of a linear equation in two variables

x

y

solution to a linear inequality

x

y

standard form of a linear equation

vertical line

x

##

Key Concepts

• Points on the Axes Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates $(a,0).$ Points with an x-coordinate equal to $0$ are on the y-axis, and have coordinates $(0,b).$

• Quadrant

• Graph of a Linear Equation: The graph of a linear equation $Ax+By=C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

• How to graph a linear equation by plotting points. Step 1. Find three points whose coordinates are solutions to the equation. Organize them in a table. Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work. Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

• x-intercept and y-intercept of a Line The x-intercept is the point $(a,0)$ where the line crosses the x-axis. The y-intercept is the point $(0,b)$ where the line crosses the y-axis.

• Find the x- and y-intercepts from the Equation of a Line Use the equation of the line. To find: the x-intercept of the line, let $y=0$ and solve for x. the y-intercept of the line, let $x=0$ and solve for y.

• How to graph a linear equation using the intercepts. Step 1. Find the x- and y-intercepts of the line. Let $y=0$ and solve for x. Let $x=0$ and solve for y. Step 2. Find a third solution to the equation. Step 3. Plot the three points and check that they line up. Step 4. Draw the line

• Slope of a Line The slope of a line is $m=\frac{\mathrm{rise}}{\mathrm{run}}.$ The rise measures the vertical change and the run measures the horizontal change.

• How to find the slope of a line from its graph using $m=\frac{\mathrm{rise}}{\mathrm{run}}.$ Step 1. Locate two points on the line whose coordinates are integers. Step 2. Starting with one point, sketch a right triangle, going from the first point to the second point. Step 3. Count the rise and the run on the legs of the triangle. Step 4. Take the ratio of rise to run to find the slope: $m=\frac{\mathrm{rise}}{\mathrm{run}}.$

• Slope of a line between two points. The slope of the line between two points $({x}_{1},{y}_{1})$ and $({x}_{2},{y}_{2})$ is:

• How to graph a line given a point and the slope. Step 1. Plot the given point. Step 2. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 3. Starting at the given point, count out the rise and run to mark the second point. Step 4. Connect the points with a line.

• Slope Intercept Form of an Equation of a Line The slope–intercept form of an equation of a line with slope m and y-intercept, $(0,b)$ is $y=mx+b$

• Parallel Lines Parallel lines are lines in the same plane that do not intersect. Parallel lines have the same slope and different y-intercepts. If ${m}_{1}$ and ${m}_{2}$ are the slopes of two parallel lines then ${m}_{1}={m}_{2}.$ Parallel vertical lines have different x-intercepts.

• Perpendicular Lines Perpendicular lines are lines in the same plane that form a right angle. If ${m}_{1}$ and ${m}_{2}$ are the slopes of two perpendicular lines, then: their slopes are negative reciprocals of each other, ${m}_{1}=-\frac{1}{{m}_{2}}.$ the product of their slopes is $-1,$${m}_{1}\cdot{m}_{2}=-1.$ A vertical line and a horizontal line are always perpendicular to each other.

• How to find an equation of a line given the slope and a point. Step 1. Identify the slope. Step 2. Identify the point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1}).$ Step 4. Write the equation in slope-intercept form.

• How to find an equation of a line given two points. Step 1. Find the slope using the given points. $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ Step 2. Choose one point. Step 3. Substitute the values into the point-slope form: $y-{y}_{1}=m(x-{x}_{1}).$ Step 4. Write the equation in slope-intercept form. To Write an Equation of a LineIf given: Use: Form: Slope and y-intercept slope-intercept $y=mx+b$ Slope and a point point-slope $y-{y}_{1}=m(x-{x}_{1})$ Two points point-slope $y-{y}_{1}=m(x-{x}_{1})$

• How to find an equation of a line parallel to a given line. Step 1. Find the slope of the given line. Step 2. Find the slope of the parallel line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form: $y-{y}_{1}=m(x-{x}_{1}).$ Step 5. Write the equation in slope-intercept form

• How to find an equation of a line perpendicular to a given line. Step 1. Find the slope of the given line. Step 2. Find the slope of the perpendicular line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$ Step 5. Write the equation in slope-intercept form.

• How to graph a linear inequality in two variables. Step 1. Identify and graph the boundary line. If the inequality is $\le\mathrm{or}\ge,$ the boundary line is solid. If the inequality is $<\,\mathrm{or}>,$ the boundary line is dashed. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality? Step 3. Shade in one side of the boundary line. If the test point is a solution, shade in the side that includes the point. If the test point is not a solution, shade in the opposite side.

• Function Notation: For the function $y=f(x)$ f is the name of the function x is the domain value $f(x)$ is the range value y corresponding to the value x We read $f(x)$ as f of x or the value of f at x.

• Independent and Dependent Variables: For the function $y=f(x),$ x is the independent variable as it can be any value in the domain y is the dependent variable as its value depends on x

• Vertical Line Test A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point. If any vertical line intersects the graph in more than one point, the graph does not represent a function.

• Graph of a Function The graph of a function is the graph of all its ordered pairs, $(x,y)$ or using function notation, $(x,f(x))$ where $y=f(x).$

• Linear Function

• Constant Function

• Identity Function

• Square Function

• Cube Function

• Square Root Function

• Absolute Value Function

##

Review Exercises

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

In the following exercises, determine which ordered pairs are solutions to the given equations.

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph each equation.

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

Find x- and *y-*Intercepts

In the following exercises, find the x- and y-intercepts.

In the following exercises, find the intercepts of each equation.

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Find the Slope of a Line

In the following exercises, find the slope of each line shown.

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

Graph a Line Using Its Slope and Intercept

In the following exercises, identify the slope and y-intercept of each line.

In the following exercises, graph the line of each equation using its slope and y-intercept.

In the following exercises, determine the most convenient method to graph each line.

Graph and Interpret Applications of Slope-Intercept

Use Slopes to Identify Parallel and Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

Find an Equation of the Line Given the Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

Find an Equation of the Line Given the Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Find an Equation of the Line Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

Find an Equation of a Line Parallel to a Given Line

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

Find an Equation of a Line Perpendicular to a Given Line

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

Graph Linear Inequalities in Two Variables

In the following exercises, graph each linear inequality.

Solve Applications using Linear Inequalities in Two Variables

Find the Domain and Range of a Relation

In the following exercises, for each relation, ⓐ find the domain of the relation ⓑ find the range of the relation.

In the following exercise, use the mapping of the relation to ⓐ list the ordered pairs of the relation ⓑ find the domain of the relation ⓒ find the range of the relation.

In the following exercise, use the graph of the relation to ⓐ list the ordered pairs of the relation ⓑ find the domain of the relation ⓒ find the range of the relation.

Determine if a Relation is a Function

In the following exercises, use the set of ordered pairs to ⓐ determine whether the relation is a function ⓑ find the domain of the relation ⓒ find the range of the relation.

In the following exercises, use the mapping to ⓐ determine whether the relation is a function ⓑ find the domain of the function ⓒ find the range of the function.

In the following exercises, determine whether each equation is a function.

Find the Value of a Function

In the following exercises, evaluate the function:

ⓐ $f(-2)$ ⓑ $f(3)$ ⓒ $f(a).$

In the following exercises, evaluate the function.

Use the Vertical line Test

In the following exercises, determine whether each graph is the graph of a function.

Identify Graphs of Basic Functions

In the following exercises, ⓐ graph each function ⓑ state its domain and range. Write the domain and range in interval notation.

Read Information from a Graph of a Function

In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation

In the following exercises, use the graph of the function to find the indicated values.

##

Find the slope of each line shown.

Graph the line for each of the following equations.

Find the equation of each line. Write the equation in slope-intercept form.

Graph each linear inequality.

In the following exercises, ⓐ graph each function ⓑ state its domain and range.Write the domain and range in interval notation.

Key Terms

boundary line

domain of a relation

x

function

A function is a relation that assigns to each element in its domain exactly one element in the range.

horizontal line

y

intercepts of a line

x

y

linear equation

A

B

linear inequality

A

B

mapping

A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.

ordered pair

x

y

origin

x

y

parallel lines

Parallel lines are lines in the same plane that do not intersect.

perpendicular lines

Perpendicular lines are lines in the same plane that form a right angle.

point-slope form

m

range of a relation

y-

relation

x

y

solution of a linear equation in two variables

x

y

solution to a linear inequality

x

y

standard form of a linear equation

vertical line

x

##

Key Concepts

• Points on the Axes Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates $(a,0).$ Points with an x-coordinate equal to $0$ are on the y-axis, and have coordinates $(0,b).$

• Quadrant

• Graph of a Linear Equation: The graph of a linear equation $Ax+By=C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

• How to graph a linear equation by plotting points. Step 1. Find three points whose coordinates are solutions to the equation. Organize them in a table. Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work. Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

• x-intercept and y-intercept of a Line The x-intercept is the point $(a,0)$ where the line crosses the x-axis. The y-intercept is the point $(0,b)$ where the line crosses the y-axis.

• Find the x- and y-intercepts from the Equation of a Line Use the equation of the line. To find: the x-intercept of the line, let $y=0$ and solve for x. the y-intercept of the line, let $x=0$ and solve for y.

• How to graph a linear equation using the intercepts. Step 1. Find the x- and y-intercepts of the line. Let $y=0$ and solve for x. Let $x=0$ and solve for y. Step 2. Find a third solution to the equation. Step 3. Plot the three points and check that they line up. Step 4. Draw the line

• Slope of a Line The slope of a line is $m=\frac{\mathrm{rise}}{\mathrm{run}}.$ The rise measures the vertical change and the run measures the horizontal change.

• How to find the slope of a line from its graph using $m=\frac{\mathrm{rise}}{\mathrm{run}}.$ Step 1. Locate two points on the line whose coordinates are integers. Step 2. Starting with one point, sketch a right triangle, going from the first point to the second point. Step 3. Count the rise and the run on the legs of the triangle. Step 4. Take the ratio of rise to run to find the slope: $m=\frac{\mathrm{rise}}{\mathrm{run}}.$

• Slope of a line between two points. The slope of the line between two points $({x}_{1},{y}_{1})$ and $({x}_{2},{y}_{2})$ is:

• How to graph a line given a point and the slope. Step 1. Plot the given point. Step 2. Use the slope formula $m=\frac{\mathrm{rise}}{\mathrm{run}}$ to identify the rise and the run. Step 3. Starting at the given point, count out the rise and run to mark the second point. Step 4. Connect the points with a line.

• Slope Intercept Form of an Equation of a Line The slope–intercept form of an equation of a line with slope m and y-intercept, $(0,b)$ is $y=mx+b$

• Parallel Lines Parallel lines are lines in the same plane that do not intersect. Parallel lines have the same slope and different y-intercepts. If ${m}_{1}$ and ${m}_{2}$ are the slopes of two parallel lines then ${m}_{1}={m}_{2}.$ Parallel vertical lines have different x-intercepts.

• Perpendicular Lines Perpendicular lines are lines in the same plane that form a right angle. If ${m}_{1}$ and ${m}_{2}$ are the slopes of two perpendicular lines, then: their slopes are negative reciprocals of each other, ${m}_{1}=-\frac{1}{{m}_{2}}.$ the product of their slopes is $-1,$${m}_{1}\cdot{m}_{2}=-1.$ A vertical line and a horizontal line are always perpendicular to each other.

• How to find an equation of a line given the slope and a point. Step 1. Identify the slope. Step 2. Identify the point. Step 3. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1}).$ Step 4. Write the equation in slope-intercept form.

• How to find an equation of a line given two points. Step 1. Find the slope using the given points. $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ Step 2. Choose one point. Step 3. Substitute the values into the point-slope form: $y-{y}_{1}=m(x-{x}_{1}).$ Step 4. Write the equation in slope-intercept form. To Write an Equation of a LineIf given: Use: Form: Slope and y-intercept slope-intercept $y=mx+b$ Slope and a point point-slope $y-{y}_{1}=m(x-{x}_{1})$ Two points point-slope $y-{y}_{1}=m(x-{x}_{1})$

• How to find an equation of a line parallel to a given line. Step 1. Find the slope of the given line. Step 2. Find the slope of the parallel line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form: $y-{y}_{1}=m(x-{x}_{1}).$ Step 5. Write the equation in slope-intercept form

• How to find an equation of a line perpendicular to a given line. Step 1. Find the slope of the given line. Step 2. Find the slope of the perpendicular line. Step 3. Identify the point. Step 4. Substitute the values into the point-slope form, $y-{y}_{1}=m(x-{x}_{1})$ Step 5. Write the equation in slope-intercept form.

• How to graph a linear inequality in two variables. Step 1. Identify and graph the boundary line. If the inequality is $\le\mathrm{or}\ge,$ the boundary line is solid. If the inequality is $<\,\mathrm{or}>,$ the boundary line is dashed. Step 2. Test a point that is not on the boundary line. Is it a solution of the inequality? Step 3. Shade in one side of the boundary line. If the test point is a solution, shade in the side that includes the point. If the test point is not a solution, shade in the opposite side.

• Function Notation: For the function $y=f(x)$ f is the name of the function x is the domain value $f(x)$ is the range value y corresponding to the value x We read $f(x)$ as f of x or the value of f at x.

• Independent and Dependent Variables: For the function $y=f(x),$ x is the independent variable as it can be any value in the domain y is the dependent variable as its value depends on x

• Vertical Line Test A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point. If any vertical line intersects the graph in more than one point, the graph does not represent a function.

• Graph of a Function The graph of a function is the graph of all its ordered pairs, $(x,y)$ or using function notation, $(x,f(x))$ where $y=f(x).$

• Linear Function

• Constant Function

• Identity Function

• Square Function

• Cube Function

• Square Root Function

• Absolute Value Function

##

Review Exercises

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

In the following exercises, determine which ordered pairs are solutions to the given equations.

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph each equation.

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

Find x- and *y-*Intercepts

In the following exercises, find the x- and y-intercepts.

In the following exercises, find the intercepts of each equation.

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Find the Slope of a Line

In the following exercises, find the slope of each line shown.

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

Graph a Line Using Its Slope and Intercept

In the following exercises, identify the slope and y-intercept of each line.

In the following exercises, graph the line of each equation using its slope and y-intercept.

In the following exercises, determine the most convenient method to graph each line.

Graph and Interpret Applications of Slope-Intercept

Use Slopes to Identify Parallel and Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

Find an Equation of the Line Given the Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

Find an Equation of the Line Given the Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Find an Equation of the Line Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

Find an Equation of a Line Parallel to a Given Line

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

Find an Equation of a Line Perpendicular to a Given Line

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

Graph Linear Inequalities in Two Variables

In the following exercises, graph each linear inequality.

Solve Applications using Linear Inequalities in Two Variables

Find the Domain and Range of a Relation

In the following exercises, for each relation, ⓐ find the domain of the relation ⓑ find the range of the relation.

In the following exercise, use the mapping of the relation to ⓐ list the ordered pairs of the relation ⓑ find the domain of the relation ⓒ find the range of the relation.

In the following exercise, use the graph of the relation to ⓐ list the ordered pairs of the relation ⓑ find the domain of the relation ⓒ find the range of the relation.

Determine if a Relation is a Function

In the following exercises, use the set of ordered pairs to ⓐ determine whether the relation is a function ⓑ find the domain of the relation ⓒ find the range of the relation.

In the following exercises, use the mapping to ⓐ determine whether the relation is a function ⓑ find the domain of the function ⓒ find the range of the function.

In the following exercises, determine whether each equation is a function.

Find the Value of a Function

In the following exercises, evaluate the function:

ⓐ $f(-2)$ ⓑ $f(3)$ ⓒ $f(a).$

In the following exercises, evaluate the function.

Use the Vertical line Test

In the following exercises, determine whether each graph is the graph of a function.

Identify Graphs of Basic Functions

In the following exercises, ⓐ graph each function ⓑ state its domain and range. Write the domain and range in interval notation.

Read Information from a Graph of a Function

In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation

In the following exercises, use the graph of the function to find the indicated values.

##

Find the slope of each line shown.

Graph the line for each of the following equations.

Find the equation of each line. Write the equation in slope-intercept form.

Graph each linear inequality.

In the following exercises, ⓐ graph each function ⓑ state its domain and range.Write the domain and range in interval notation.

1. ⓐ $(-1,-5)$ⓑ $(-3,4)$ⓒ $(2,-3)$ⓓ $(1,\frac{5}{2})$

2. $5x+y=10;$ⓐ $(5,1)$ⓑ $(2,0)$ⓒ $(4,-10)$

3. $y=4x-3$

4. $y=\frac{1}{2}x+3$

5. $x-y=6$

1. $3x-2y=6$

2. $x=3$

3. $y=\frac{4}{3}x$ and $y=\frac{4}{3}$

4. $x+2y=6$

5. $y=\frac{3}{4}x-12$

1. $-x+3y=3$

2. $2x-y=5$

3. $y=4x$

4. $x=5$

5. $(3,5),(4,-1)$

1. $(2,1),(4,6)$

2. $(-3,4);$$m=-\frac{1}{3}$

3. y-intercept 1; $m=-\frac{3}{4}$

4. $y=\frac{5}{3}x-6$

5. $4x-5y=8$

1. $y=-x-1$

2. $y=-\frac{2}{5}x+3$

3. $4x-3y=12$

4. $y=-3$

5. $x-y=2$

1. $y=\frac{3}{4}x-1$

2. Marjorie teaches piano. The equation $P=35s-250$ models the relation between her weekly profit, P, in dollars and the number of student lessons, s, that she teaches.

ⓐ Find Marjorie’s profit for a week when she teaches no student lessons. ⓑ Find the profit for a week when she teaches 20 student lessons. ⓒ Interpret the slope and P-intercept of the equation. ⓓ Graph the equation.

3. $y=5x-1;10x+2y=0$

4. $2x-y=8;x-2y=4$

5. slope $-5$ and $y$-intercept $(0,-3)$

1. slope $-2$ and $y$-intercept $(0,0)$

2. $m=\frac{3}{5},$ point $(10,6)$

3. $m=-2,$ point $(-1,-3)$

4. $(7,1)$ and $(5,0)$

5. $(5,2)$ and $(-1,2)$

1. line $2x+5y=-10,$ point $(10,4)$

2. line $y=-5,$ point $(-4,3)$

3. line $2x-3y=9,$ point $(-4,0)$

4. line $x=-5$ point $(2,1)$

5. Determine whether each ordered pair is a solution to the inequality $x+y>4:$

ⓐ $(6,1)$ ⓑ $(-3,6)$ ⓒ $(3,2)$ ⓓ $(-5,10)$ ⓔ $(0,0)$

1. Write the inequality shown by the graph with the boundary line $y=\frac{2}{3}x-3.$

2. Write the inequality shown by the shaded region in the graph with the boundary line $x-2y=6.$

3. Graph the linear inequality $y\le-\frac{1}{4}x+3.$

4. Graph the linear inequality $3x+2y>10.$

5. Graph the linear inequality $y<6.$

1. Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking.

ⓐ If x is the number of minutes that Atsushi runs and y is the number minutes he bikes, find the inequality that models the situation. ⓑ Graph the inequality. ⓒ List three solutions to the inequality. What options do the solutions provide Atsushi?

2. $\mathrm{\{}(-3,7),(-2,3),(-1,9),$$(0,-3),(-1,8)\mathrm{\}}$

3. $\mathrm{\{}(-3,27),(-2,8),(-1,1),$$(0,0),(1,1),(2,8),(3,27)\mathrm{\}}$

4. $y={x}^{2}$

5. $y={x}^{3}$

1. $f(x)=3x-4$

2. $f(x)={x}^{2}-5x+6$

3. $f(x)=-4x-2$

4. $f(x)=-6$

5. $f(x)=3{x}^{2}$

1. $f(x)={x}^{2}+2$

2. $f(x)=\sqrt{x+2}$

3. $f(x)=|x|+1$

4. ⓐ Find $f(0).$ ⓑ Find $f(\frac{1}{2}\pi).$ ⓒ Find $f(-\frac{3}{2}\pi).$ ⓓ Find the values for x when $f(x)=0.$ ⓔ Find the $x$-intercepts. ⓕ Find the $y$-intercepts. ⓖ Find the domain. Write it in interval notation. ⓗ Find the range. Write it in interval notation.

5. Plot each point in a rectangular coordinate system.

ⓐ $(2,5)$ ⓑ $(-1,-3)$ ⓒ $(0,2)$ ⓓ $(-4,\frac{3}{2})$ ⓔ $(5,0)$

1. ⓐ

ⓑ

2. Graph the line with slope $\frac{1}{2}$ containing the point $(-3,-4).$

3. $y=\frac{5}{3}x-1$

4. $y=2$

5. $m=2,$ point $(-3,-1)$

1. perpendicular to the line $y=\frac{5}{4}x+2,$ containing the point $(-10,3)$

2. $y>\frac{3}{2}x+5$

3. $y\le-5x$

4. Use the set of ordered pairs to ⓐ determine whether the relation is a function, ⓑ find the domain of the relation, and ⓒ find the range of the relation.

$\mathrm{\{}(-3,27),(-2,8),(-1,1),(0,0),$$(1,1),(2,8),(3,27)\mathrm{\}}$

5. $f(x)={x}^{2}+1$

1. ⓐ Find the $x$-intercepts. ⓑ Find the $y$-intercepts. ⓒ Find $f(-1).$ ⓓ Find $f(1).$ ⓔ Find the domain. Write it in interval notation. ⓕ Find the range. Write it in interval notation.