3.1E: 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?

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.

10.

11.

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.

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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