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Mathematics LibreTexts

3.2E: Functions and Function Notation (Exercises)

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For the following exercises, determine whether the relation is a function.

1. \{(a, b),(c, d),(e, d)\}
2. \{(5,2),(6,1),(6,2),(4,8)\}\)
3. y^{2}+4=x, for x the independent variable and y the dependent variable
4. Is the graph in Figure 1 a function?

Graph of a parabola.

For the following exercises, evaluate the function at the indicated values:

\begin{array}{lllll} f(-3) ; & f(2) ; & f(-a) ; & -f(a) ; & f(a+h) .\end{array} \nonumber

5. f(x)=-2 x^{2}+3 x
6. f(x)=2|3 x-1|

For the following exercises, determine whether the functions are one-to-one.

7. f(x)=-3 x+5
8. f(x)=\mid x-3

For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function.

9.

Graph of a cubic function.

10.

Graph of a relation.

11.

Graph of a relation.

For the following exercises, graph the functions.

12. f(x)=\mid x+1
13. f(x)=x^{2}-2

For the following exercises, use Figure 2 to approximate the values.

Graph of a parabola.

14. f(2)
15. f(-2)
16. If f(x)=-2, then solve for x.
17. If f(x)=1, then solve for x.

For the following exercises, use the function h(t)=-16 t^{2}+80 t to find the values in simplest form.

18. \frac{h(2)-h(1)}{2-1}
19. \frac{h(a)-h(1)}{a-1}


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