For the following exercises, determine whether each of the following relations is a function.

1. y = 2x + 8

2. [latex]\left\{\left(2,1\right),\left(3,2\right),\left(-1,1\right),\left(0,-2\right)\right\}[/latex]

For the following exercises, evaluate the function [latex]f\left(x\right)=-3{x}^{2}+2x[/latex] at the given input.

3. [latex]f\left(-2\right)[/latex]

4. [latex]f\left(a\right)[/latex]

5. Show that the function [latex]f\left(x\right)=-2{\left(x - 1\right)}^{2}+3[/latex] is not one-to-one.

6. Write the domain of the function [latex]f\left(x\right)=\sqrt{3-x}[/latex] in interval notation.

7. Given [latex]f\left(x\right)=2{x}^{2}-5x[/latex], find [latex]f\left(a+1\right)-f\left(1\right)[/latex].

8. Graph the function [latex]\begin{cases}f\left(x\right) & =x+1 & \text{ if }-2 < x < 3 \\ \text{ }& =-x & \text{ if }x\ge 3\end{cases}[/latex]

For the following exercises, use the graph of the piecewise-defined function shown below.

9. Find [latex]f\left(2\right)[/latex].

10. Find [latex]f\left(-2\right)[/latex].

For the following exercises, use the values listed below.

11. Solve the equation [latex]F\left(x\right)=5[/latex].

12. Find [latex]F\left(6\right)[/latex].

13. Is the function represented by the table one-to-one?

See the next page for the solutions to the odd-numbered problems.