Section 1
Graphs and Graphing Utilities
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(1,4)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(2,5)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(-2,3)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(-1,4)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(-3,-5)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(-4,-2)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(4,-1)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(3,-2)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(-4,0)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$(0,-3)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$\left(\frac{7}{2},-\frac{3}{2}\right)$$
In Exercises 1–12, plot the given point in a rectangular coordinate system.$$\left(-\frac{5}{2}, \frac{3}{2}\right)$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x^{2}-2$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x^{2}+2$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x-2$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x+2$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=2 x+1$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=2 x-4$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=-\frac{1}{2} x$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=-\frac{1}{2} x+2$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=2|x|$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=-2|x|$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=|x|+1$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=|x|-1$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=9-x^{2}$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=-x^{2}$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x^{3}$$
Graph each equation in Exercises $13-28 .$ Let $x=-3,-2,-1,0$ $1,2,$ and 3.$$y=x^{3}-1$$
In Exercises 29–32, match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-5,5,1] \text { by }[-5,5,1]$$A. (GRAPH NOT COPY)B. (GRAPH NOT COPY)C. (GRAPH NOT COPY)
In Exercises 29–32, match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-10,10,2] \text { by }[-4,4,2]$$A. (GRAPH NOT COPY)B. (GRAPH NOT COPY)C. (GRAPH NOT COPY)
In Exercises 29–32, match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-20,80,10] \text { by }[-30,70,10]$$A. (GRAPH NOT COPY)B. (GRAPH NOT COPY)C. (GRAPH NOT COPY)
In Exercises 29–32, match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-40,40,20] \text { by }[-1000,1000,100]$$A. (GRAPH NOT COPY)B. (GRAPH NOT COPY)C. (GRAPH NOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.Which equation corresponds to $Y_{2}$ in the table?A. $y_{2}=x+8$B. $y_{2}=x-2$C. $y_{2}=2-x$D. $y_{2}=1-2 x$
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.Which equation corresponds to $Y_{1}$ in the table?A. $y_{1}=-3 x$B. $y_{1}=x^{2}$C. $y_{1}=-x^{2}$D. $y_{1}=2-x$
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.Does the graph of $\mathrm{Y}_{2}$ pass through the origin?
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.Does the graph of $Y_{1}$ pass through the origin?
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.At which point does the graph of $Y_{2}$ cross the $x$ -axis?
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.At which point does the graph of $Y_{2}$ cross the $y$ -axis?
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.At which points do the graphs of $Y_{1}$ and $Y_{2}$ intersect?
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve Exercises 33–40.For which values of $x$ is $Y_{1}=Y_{2} ?$
In Exercises $41-46,$ use the graph to a. determine the$x$ -intercepts, if any; b. determine the $y$ -intercepts, if any. For each graph, tick marks along the axes represent one unit each.
Write each English sentence as an equation in two variables. Then graph the equation.The $y$ -value is four more than twice the $x$ -value.
write each English sentence as an equation in two variables. Then graph the equation.The $y$ -value is the difference between four and twice the $x$ -value.
write each English sentence as an equation in two variables. Then graph the equation.The $y$ -value is three decreased by the square of the $x$ -value.
write each English sentence as an equation in two variables. Then graph the equation.The $y$ -value is two more than the square of the $x$ -value.
Graph each equation.$y=5(\text { Let } x=-3,-2,-1,0,1,2, \text { and } 3 .)$
Graph each equation.$y=-1 \text { (Let } x=-3,-2,-1,0,1,2, \text { and } 3 .)$
Graph each equation.$y=\frac{1}{x}\left(\text { Let } x=-2,-1,-\frac{1}{2},-\frac{1}{3}, \frac{1}{3}, \frac{1}{2}, 1, \text { and } 2 .\right)$
Graph each equation.$y=-\frac{1}{x}\left(\text { Let } x=-2,-1,-\frac{1}{2},-\frac{1}{3}, \frac{1}{3}, \frac{1}{2}, 1, \text { and } 2 .\right)$
Use this information to solve Exercises.A. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in 2010.B. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2010 .$ How does this compare with your estimate in part (a)?C. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in 2010.D. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2010 .$ How does this compare with your estimate in part (c)?E. For the period from 1990 through $2014,$ in which year was marijuana use by seniors at a maximum? Estimate the percentage of seniors who used marijuana in that year.
Use this information to solve Exercises $55-56$.A. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in 2014.B. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2014 .$ How does this compare with your estimate in part (a)?C. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in 2014.D. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2014 .$ How does this compare with your estimate in part (c)?E. For the period from 1990 through $2014,$ in which year was alcohol use by seniors at a maximum? What percentage of seniors used alcohol in that year.
Contrary to popular belief, older people do not need less sleep than younger adults. However, the line graphs show that they awaken more often during the night. The numerous awakenings are one reason why some elderly individuals report that sleep is less restful than it had been in the past. Use the line graphs to solve Exercises $57-60$.At which age, estimated to the nearest year, do women have the least number of awakenings during the night? What is the average number of awakenings at that age?
Contrary to popular belief, older people do not need less sleep than younger adults. However, the line graphs show that they awaken more often during the night. The numerous awakenings are one reason why some elderly individuals report that sleep is less restful than it had been in the past. Use the line graphs to solve Exercises $57-60$.At which age do men have the greatest number of awakenings during the night? What is the average number of awakenings at that age?
Contrary to popular belief, older people do not need less sleep than younger adults. However, the line graphs show that they awaken more often during the night. The numerous awakenings are one reason why some elderly individuals report that sleep is less restful than it had been in the past. Use the line graphs to solve Exercises $57-60$.Estimate, to the nearest tenth, the difference between the average number of awakenings during the night for $25-$ year-old men and 25 -year-old women.
Contrary to popular belief, older people do not need less sleep than younger adults. However, the line graphs show that they awaken more often during the night. The numerous awakenings are one reason why some elderly individuals report that sleep is less restful than it had been in the past. Use the line graphs to solve Exercises $57-60$.Estimate, to the nearest tenth, the difference between the average number of awakenings during the night for 18 -year-old men and 18 -year-old women.
Explaining the ConceptsWhat is the rectangular coordinate system?
Explaining the ConceptsExplain how to plot a point in the rectangular coordinate system. Give an example with your explanation.
Explaining the ConceptsExplain why $(5,-2)$ and $(-2,5)$ do not represent the same point.
Explain how to graph an equation in the rectangular coordinate system.
Explaining the ConceptsWhat does a $[-20,2,1]$ by $[-4,5,0.5]$ viewing rectangle mean?
Technology ExerciseUse a graphing utility to verify each of your hand-drawn graphs in Exercises $13-28 .$ Experiment with the settings for the viewing rectangle to make the graph displayed by the graphing utility resemble your hand-drawn graph as much as possible.
determine whether each statement makes sense or does not make sense, and explain your reasoning.The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.
Determine whether each statement makes sense or does not make sense, and explain your reasoning.There is something wrong with my graphing utility because it is not displaying numbers along the $x$ - and $y$ -axes.
Determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the ordered pairs $(-2,2),(0,0),$ and $(2,2)$ to graph a straight line.
Determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the ordered pairs (time of day, calories that I burned)to obtain a graph that is a horizontal line.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If the product of a point's coordinates is positive, the point must be in quadrant I.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If a point is on the $x$ -axis, it is neither up nor down, so $x=0$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If a point is on the $y$ -axis, its $x$ -coordinate must be $0 .$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The ordered pair $(2,5)$ satisfies $3 y-2 x=-4$.
List the quadrant or quadrants satisfying each condition.$$x y>0$$
In Exercises $75-78,$ list the quadrant or quadrants satisfying each condition.$$\frac{y}{x}<0$$
In Exercises $75-78,$ list the quadrant or quadrants satisfying each condition.$x^{3}>0$ and $y^{3}<0$
In Exercises $75-78,$ list the quadrant or quadrants satisfying each condition.$x^{3}<0$ and $y^{3}>0$
In Exercises $79-82,$ match the story with the correct figure. The figures are labeled $(a),(b),(c),$ and $(d)$As the blizzard got worse, the snow fell harder and harder.
In Exercises $79-82,$ match the story with the correct figure. The figures are labeled $(a),(b),(c),$ and $(d)$.The snow fell more and more softly.
In Exercises $79-82,$ match the story with the correct figure. The figures are labeled $(a),(b),(c),$ and $(d)$It snowed hard, but then it stopped. After a short time, the snow started falling softly.
Match the story with the correct figure. The figures are labeled $(a),(b),(c),$ and $(d)$It snowed softly, and then it stopped. After a short time, the snow started falling hard.
Select the graph that best illustrates each story.An airplane flew from Miami to San Francisco.
Select the graph that best illustrates each story.At noon, you begin to breathe in.
Select the graph that best illustrates each story.Measurements are taken of a person's height from birth to age 100.
Equations and InequalitiesYou begin your bike ride by riding down a hill. Then you ride up another hill. Finally, you ride along a level surface before coming to a stop.
Will help you prepare for the material covered in the next section.If 6 is substituted for $x$ in the equation$$2(x-3)-17=13-3(x+2)$$is the resulting statement true or false?
Exercises $87-89$ will help you prepare for the material covered in the next section.Multiply and simplify: $12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)$
Exercises $87-89$ will help you prepare for the material covered in the next section.Multiply and simplify: $(x-3)\left(\frac{3}{x-3}+9\right)$