# 1.9 Practice Questions

## Verbal Questions

1. What is the difference between a relation and a function?
2. What is the difference between the input and the output of a function?
3. Why does the vertical line test tell us whether the graph of a relation represents a function?
4. How can you determine if a relation is a one-to-one function?
5. Why does the horizontal line test tell us whether the graph of a function is one-to-one?

Odd Number Verbal Solutions

## Algebraic Questions

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

1. $\left\{\left(a,b\right),\text{ }\left(c,d\right),\text{ }\left(a,c\right)\right\}$
2. $\left\{\left(a,b\right),\left(b,c\right),\left(c,c\right)\right\}$

For the following exercises, determine whether the relation represents $\text{}y\text{}$ as a function of $\text{}x\text{}$.

1. $5x+2y=10$
2. $y={x}^{2}$
3. $x={y}^{2}$
4. $3{x}^{2}+y=14$
5. $2x+{y}^{2}=6$
6. $y=-2{x}^{2}+40x$
7. $y=\frac{1}{x}$
8. $x=\frac{3y+5}{7y-1}$
9. $x=\sqrt{1-{y}^{2}}$
10. $y=\frac{3x+5}{7x-1}$
11. ${x}^{2}+{y}^{2}=9$
12. $2xy=1$
13. $x={y}^{3}$
14. $y={x}^{3}$
15. $y=\sqrt{1-{x}^{2}}$
16. $x=±\sqrt{1-y}$
17. $y=±\sqrt{1-x}$
18. ${y}^{2}={x}^{2}$
19. ${y}^{3}={x}^{2}$

For the following exercises, evaluate the function $\text{}f\text{}$ at the indicated values $\text{ }f\left(-3\right),f\left(2\right),f\left(-a\right),-f\left(a\right),f\left(a+h\right)$.

1. $f\left(x\right)=2x-5$
2. $f\left(x\right)=-5{x}^{2}+2x-1$
3. $f\left(x\right)=\sqrt{2-x}+5$
4. $f\left(x\right)=\frac{6x-1}{5x+2}$
5. $f\left(x\right)=|x-1|-|x+1|$
6. Given the function $\text{}g\left(x\right)=5-{x}^{2},\text{}$ evaluate $\text{}\frac{g\left(x+h\right)-g\left(x\right)}{h},\text{}h\ne 0$
7. Given the function $\text{}g\left(x\right)={x}^{2}+2x,\text{}$ evaluate $\text{}\frac{g\left(x\right)-g\left(a\right)}{x-a},\text{}x\ne a$
8. Given the function $\text{}k\left(t\right)=2t-1:$
1. Evaluate $\text{}k\left(2\right)$
2. Solve $\text{}k\left(t\right)=7$
9. Given the function $\text{}f\left(x\right)=8-3x:$
1. Evaluate $\text{}f\left(-2\right)$
2. Solve $\text{}f\left(x\right)=-1$
10. Given the function $\text{}p\left(c\right)={c}^{2}+c:$
1. Evaluate $\text{}p\left(-3\right)$
2. Solve $\text{}p\left(c\right)=2$
11. Given the function $\text{}f\left(x\right)={x}^{2}-3x:$
1. Evaluate $\text{}f\left(5\right)$
2. Solve $\text{}f\left(x\right)=4$
12. Given the function $\text{}f\left(x\right)=\sqrt{x+2}:$
1. Evaluate $\text{}f\left(7\right)$
2. Solve $\text{}f\left(x\right)=4$
13. Consider the relationship $\text{}3r+2t=18$
1. Write the relationship as a function $\text{}r=f\left(t\right)$
2. Evaluate $\text{}f\left(-3\right)$
3. Solve $\text{}f\left(t\right)=2$

Odd Number Algebraic Solutions

## Graphical Questions

For the following exercises, use the vertical line test to determine which graphs show relations that are functions.

1. Given the following graph,
1. Evaluate $\text{}f\left(-1\right)$.
2. Solve for $\text{}f\left(x\right)=3$.
2. Given the following graph,
1. Evaluate $\text{}f\left(0\right)$.
2. Solve for $\text{}f\left(x\right)=-3$.
3. Given the following graph,
1. Evaluate $\text{}f\left(4\right)$.
2. Solve for $\text{}f\left(x\right)=1$.

For the following exercises, determine if the given graph is a one-to-one function.

Odd Number Graphical Solutions

## Numeric Questions

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

1. $\left\{\left(-1,-1\right),\left(-2,-2\right),\left(-3,-3\right)\right\}$
2. $\left\{\left(3,4\right),\left(4,5\right),\left(5,6\right)\right\}$
3. $\left\{\left(2,5\right),\left(7,11\right),\left(15,8\right),\left(7,9\right)\right\}$

For the following exercises, determine if the relation represented in table form represents $\text{}y\text{}$ as a function of $\text{}x$.

1.  $x$ $y$ 5 10 15 3 8 14
2.  $x$ $y$ 5 10 15 3 8 8
3.  $x$ $y$ 5 10 10 3 8 14

For the following exercises, use the function $\text{}f\text{}$ represented in Table 1-14.

Table 1-14
$x$ $f\left(x\right)$
0 74
1 28
2 1
3 53
4 56
5 3
6 36
7 45
8 14
9 47
1. Evaluate $\text{}f\left(3\right)$.
2. Solve $\text{}f\left(x\right)=1$.

For the following exercises, evaluate the function $\text{}f\text{}$ at the values $f\left(-2\right),\text{}f\left(-1\right),\text{}f\left(0\right),\text{}f\left(1\right)$ and $\text{}f\left(2\right)$.

1. $f\left(x\right)=4-2x$
2. $f\left(x\right)=8-3x$
3. $f\left(x\right)=8{x}^{2}-7x+3$
4. $f\left(x\right)=3+\sqrt{x+3}$
5. $f\left(x\right)=\frac{x-2}{x+3}$
6. $f\left(x\right)={3}^{x}$

For the following exercises, evaluate the expressions, given functions $f,\text{}\text{}g$, and $\text{}h:$

• $f\left(x\right)=3x-2$
• $g\left(x\right)=5-{x}^{2}$
• $h\left(x\right)=-2{x}^{2}+3x-1$
1. $3f\left(1\right)-4g\left(-2\right)$
2. $f\left(\frac{7}{3}\right)-h\left(-2\right)$

Odd Number Numeric Solutions

## Technology Questions

For the following exercises, graph $\text{}y={x}^{2}\text{}$ on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.

1. $\left[-0.1,\text{ }0.1\right]$
2. $\left[-10,\text{ 10}\right]$
3. $\left[-100,100\right]$

For the following exercises, graph $\text{}y={x}^{3}\text{}$ on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.

1. $\left[-0.1,\text{ 0}\text{.1}\right]$
2. $\left[-10,\text{ 10}\right]$
3. $\left[-100,\text{ 100}\right]$

For the following exercises, graph $\text{}y=\sqrt{x}\text{}$ on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.

1. $\left[0,\text{ 0}\text{.01}\right]$
2. $\left[0,\text{ 100}\right]$
3. $\left[0,\text{ 10,000}\right]$

For the following exercises, graph $y=\sqrt[3]{x}$ on the given viewing window. Determine the corresponding range for each viewing window. Show each graph.

1. $\left[-0.001,\text{0.001}\right]$
2. $\left[-1000,\text{1000}\right]$
3. $\left[-1,000,000,\text{1,000,000}\right]$

Odd Number Technology Solutions

## Real-World Applications Questions

1. The amount of garbage, $\text{}G,\text{}$ produced by a city with population $\text{}p\text{}$ is given by $\text{}G=f\left(p\right)\text{}$. $G\text{}$ is measured in tons per week, and $\text{}p\text{}$ is measured in thousands of people.
1. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function $\text{}f\text{}$.
2. Explain the meaning of the statement $\text{}f\left(5\right)=2$.
2. The number of cubic yards of dirt, $\text{}D,\text{}$ needed to cover a garden with area $\text{}a\text{}$ square feet is given by $\text{}D=g\left(a\right)$.
1. A garden with area 5000 ft2 requires 50 yd3 of dirt. Express this information in terms of the function $\text{}g$.
2. Explain the meaning of the statement $\text{}g\left(100\right)=1$.
3. Let $\text{}f\left(t\right)\text{}$ be the number of ducks in a lake $\text{}t\text{}$ years after 1990. Explain the meaning of each statement:
1. $f\left(5\right)=30$
2. $f\left(10\right)=40$
4. Let $\text{}h\left(t\right)\text{}$ be the height above ground, in feet, of a rocket $\text{}t\text{}$ seconds after launching. Explain the meaning of each statement:
1. $h\left(1\right)=200$
2. $h\left(2\right)=350$
5. Show that the function $\text{}f\left(x\right)=3{\left(x-5\right)}^{2}+7\text{}$ is not one-to-one.

Odd Number Real-World Application Solutions