(0, 5) is the midpoint of the line segment joining $(-3,1)$ and (3, 11).

The equation ${(x+2)}^2+{(y+3)}^2=5$ is the equation of a circle with center (2, 3) and radius 5.

If a graph is symmetric with respect to the x-axis and the y-axis, then it must be symmetric with respect to the origin.

If a graph is symmetric with respect to the origin, then it must be symmetric with respect to the x-axis and the y-axis.

In the graph of the equation of the line $3y=4x+9,$ the slope is 4 and the y-intercept is 9.

If the slope of a line is 2, then the slope of any line perpendicular to it is ${\displaystyle \frac{1}{2}}.$

The slope of a vertical line is undefined.

The equation ${(x-2)}^2+{(y+3)}^2=-25$ is the equation of a circle with center $(2,-3)$ and radius 5.

$P(3,5),Q(-1,3)$

$P(-3,5),Q(3,-1)$

$P(4,-3),Q(9,-8)$

$P(2,3),Q(-7,-8)$

$P(2,-7),Q(5,-2)$

$P(-5,4),Q(10,-3)$

Show that the points $A(0,5),B(-2,-3),$ and C(3, 0) are the vertices of a right triangle.

Show that the points $A(1,2),B(4,8),C(7,-1),$ and D(10, 5) are the vertices of a rhombus.

Which of the points $(-6,3)$ and (4, 5) is closer to the origin?

Which of the points $(-6,4)$ and (5, 10) is closer to the point $(2,3)?$

Find a point on the x-axis that is equidistant from the points $(-5,3)$ and (4, 7).

Find a point on the y-axis that is equidistant from the points $(-3,-2)$ and $(2,-1).$

$x+2y=4$

$3x-4y=12$

$y=-2x^2$

$x=-y^2$

$y=x^3$

$x=-y^3$

$y=x^2+2$

$y=1-x^2$

$x^2+y^2=16$

$y=x^4-4$

Center $(2,-3),$ radius 5

Diameter with endpoints (5, 2) and $(-5,4)$

Center $(-2,-5),$ touching the y-axis

$2x-5y=10$

${\displaystyle \frac{x}{2}}-{\displaystyle \frac{y}{5}}=1$

${(x+1)}^2+{(y-3)}^2=16$

$x^2+y^2-2x+4y-4=0$

$3x^2+3y^2-6x-6=0$

Passing through (1, 2) with slope $-2$

x-intercept 2, y-intercept 5

Passing through (1, 3) and $(-1,7)$

Passing through (1, 3), perpendicular to the x-axis

Determine whether the lines in each pair are parallel, perpendicular, or neither.

1. $y=3x-2$ and $y=3x+2$

2. $3x-5y+7=0$ and $5x-3y+2=0$

3. $ax+by+c=0$ and $bx-ay+d=0$

4. $y+2={\displaystyle \frac{1}{3}}(x-3)$ and $y-5=3(x-3)$

Write the point–slope form of the equation of the line shown in the figure that is

1. Parallel to the line in the figure with x-intercept 4.

2. Perpendicular to the line in the figure with y-intercept 1.

$\{(0,1),(-1,2),(1,0),(2,-1)\}$

$\{(0,1),(0,-1),(3,2),(3,-2)\}$

$x-y=1$

$y=\sqrt{x-2}$

$x^2+y^2=0.04$

$x=-\sqrt{y}$

$x=1$

$y=2$

$y=|x+1|$

$x=y^2+1$

$f(-2)$

$g(-2)$

x if $f(x)=4$

x if $g(x)=2$

$(f+g)(1)$

$(f-g)(-1)$

$(f\cdot g)(-2)$

$(g\cdot f)(0)$

$(f\circ g)(3)$

$(g\circ f)(-2)$

$(f\circ g)(x)$

$(g\circ f)(x)$

$(f\circ f)(x)$

$(g\circ g)(x)$

$f(a+h)$

$g(a-h)$

${\displaystyle \frac{f(x+h)-f(x)}{h}}$

${\displaystyle \frac{g(x+h)-g(x)}{h}}$

$f(x)=-3$

$f(x)=x^2-2$

$g(x)=\sqrt{3x-2}$

$h(x)=\sqrt{36-x^2}$

$f(x)=\{\begin{array}{lll}x+1& \text{if}& x\ge 0\\ -x+1& \text{if}& x<0\end{array}$

$g(x)=\{\begin{array}{lll}x& \text{if}& x\ge 0\\ x^2& \text{if}& x<0\end{array}$

$f(x)=\sqrt{x},g(x)=\sqrt{x+1}$

$f(x)=|x|,g(x)=2|x-1|+3$

$f(x)={\displaystyle \frac{1}{x}},g(x)=-{\displaystyle \frac{1}{x-2}}$

$f(x)=x^2,g(x)={(x+1)}^2-2$

$f(x)=x^2-x^4$

$f(x)=x^3+x$

$f(x)=|x|+3$

$f(x)=3x+5$

$f(x)=\sqrt{x}$

$f(x)={\displaystyle \frac{2}{x}}$

$f(x)=\sqrt{x^2-4}$

$g(x)={(x^2-x+2)}^{50}$

$h(x)=\sqrt{{\displaystyle \frac{x-3}{2x+5}}}$

$H(x)={(2x-1)}^3+5$

$f(x)=x+2$

$f(x)=-2x+3$

$f(x)=\sqrt[3]{x-2}$

$f(x)=8x^3-1$

$f(x)={\displaystyle \frac{x-1}{x+2}},x\ne -2$

$f(x)={\displaystyle \frac{2x+3}{x-1}},x\ne 1$

For the graph of a function f shown in the figure,

1. Write a formula for f as a piecewise function.

2. Find the domain and range of f.

3. Find the intercepts of the graph of f.

4. Draw the graph of $y=f(-x).$

5. Draw the graph of $y=-f(x).$

6. Draw the graph of $y=f(x)+1.$

7. Draw the graph of $y=f(x+1).$

8. Draw the graph of $y=2f(x).$

9. Draw the graph of $y=f(2x).$

10. Draw the graph of $y=f\left({\displaystyle \frac{1}{2}}x\right).$

11. Explain why f is one-to-one.

12. Draw the graph of $y=f^{-1}(x).$

Scuba diving. The pressure P on the body of a scuba diver increases linearly as she descends to greater depths d in seawater. The pressure at a depth of 10 feet is 19.2 pounds per square inch, and the pressure at a depth of 25 feet is 25.95 pounds per square inch.

1. Write the equation relating P and d (with d as the independent variable) in slope–intercept form.

2. What is the meaning of the slope and the y-intercept in part (a)?

3. Determine the pressure on a scuba diver who is at a depth of 160 feet.

4. Find the depth at which the pressure on the body of the scuba diver is 104.7 pounds per square inch.

Waste disposal. The Sioux Falls, South Dakota, council considered the following data regarding the cost of disposing of waste material.

Assume that the cost C (in dollars) is linearly related to the waste w (in pounds).

1. Write the linear equation relating C and w in slope–intercept form.

2. Explain the meaning of the slope and the intercepts of the equation in part (a).

3. Suppose the city has projected 609,000 pounds of waste for the year 2008. Calculate the projected cost of disposing of the waste for 2008.

4. Suppose the city’s projected budget for waste collection in 2012 is $1 million. How many pounds of waste can be handled?

Checking your speedometer. A common way to check the accuracy of your speedometer is to drive one or more measured (not odometer) miles, holding the speedometer at a constant 60 miles per hour and checking your watch at the start and end of the measured distance.

1. How does your watch show you whether the speedometer is accurate? What mathematics is involved?

2. Why shouldn’t you use your odometer to measure the number of miles?

Playing blackjack. Chloe, a bright mathematician, read a book on counting cards in blackjack and went to Las Vegas to try her luck. She started with $100 and discovered that the amount of money she had at time t hours after the start of the game could be expressed by the function $f(t)=100+55t-3t^2.$

1. What amount of money had Chloe won or lost in the first two hours?

2. What was the average rate at which Chloe was winning or losing money during the first two hours?

3. Did she lose all of her money? If so, when?

4. If she played until she lost all of her money, what was the average rate at which she was losing her money?

Volume discounting. Major cola distributors sell a case (containing 24 cans) of cola to a retailer at a price of $4. They offer a discount of 20% for purchases over 100 cases and a discount of 25% for purchases over 500 cases. Write a piecewise function that describes this pricing scheme. Use x as the number of cases purchased and f(x) as the price paid.

Air pollution. The daily level L of carbon monoxide in a city is a function of the number of automobiles in the city. Suppose $L(x)=0.5\sqrt{x^2+4},$ where x is the number of automobiles (in hundred thousands). Suppose further that the number of automobiles in a given city is growing according to the formula $x(t)=1+0.002t^2,$ where t is time in years measured from now.

1. Form a composite function describing the daily pollution level as a function of time.

2. What pollution level is expected in five years?

Toy manufacturing. After being in business for t years, a toy manufacturer is making $x=5000+50t+10t^2$ GI Jimmy toys per year. The sale price p in dollars per toy has risen according to the formula $p=10+0.5t.$ Write a formula for the manufacturer’s yearly revenue as

1. A function of time t.

2. A function of price p.

Height and weight of NBA players The table shows the roster for the National Basketball Association (NBA) team Boston Celtics for 2012.

1. Use a graphing utility to find the line of regression relating the variables x (height in inches) and y (weight in pounds).

2. Use a graphing utility to plot the points and graph the regression line.

3. Use the line in part (a) to predict the weight of an NBA player whose height is 76 inches.