Calculus Volume 1 · free preview
Review of Functions
A function assigns to each input in its domain exactly one output in its range, and its graph is the picture of every input-output pair, readable for domain, range, intercepts, and symmetry.
1. The function idea
The function idea
2. Domain and range
Domain and range
3. Reading graphs
Reading graphs
4. Function notation in practice
Function notation in practice
5. Which relation is a function
Which of the following relations between real numbers x and y is a function of x?
6. Domain of a rational formula
What is the domain of the function f(x) = 1/(x - 3)?
7. The vertical line test
What does the vertical line test determine about a drawn curve?
8. Identifying an even function
Which function is even, meaning its graph mirrors across the vertical axis?
9. Range of a shifted parabola
What is the range of the function f(x) = (x - 1)^2 + 4?
10. Difference quotient for x squared
For f(x) = x^2, what does the difference quotient (f(x+h) - f(x))/h simplify to?
11. Domain of a square root
The function g(x) = sqrt(x - 2) is defined only when its radicand is nonnegative. What is the smallest real number in its domain? Answer with a number.
12. Value of a piecewise rule
The function f(x) = x^2 + 1 is evaluated at x = 3. What number does f(3) equal? Answer with a number.
13. Zeros of a shifted square
The function f(x) = (x - 4)^2 has exactly one zero. What is that zero? Answer with a number.
14. Symmetry classification
A function satisfies f(-x) = -f(x) for every input. What single word names this kind of symmetry? Answer in lowercase.
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