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Section 1
Graphs and Graphing Utilities
Plot the given point in a rectangular coordinate system.$$(1,4)$$
Plot the given point in a rectangular coordinate system. $$ (2,5) $$
Plot the given point in a rectangular coordinate system.$$ (-2,3) $$
Plot the given point in a rectangular coordinate system.$$ (-1,4) $$
Plot the given point in a rectangular coordinate system.$$ (-3,-5) $$
Plot the given point in a rectangular coordinate system.$$ (-4,-2) $$
Plot the given point in a rectangular coordinate system.$$ (4,-1) $$
Plot the given point in a rectangular coordinate system.$$ (3,-2) $$
Plot the given point in a rectangular coordinate system. $$ (-4,0) $$
Plot the given point in a rectangular coordinate system. $$ (0,-3) $$
Plot the given point in a rectangular coordinate system. $$ \left(\frac{7}{2},-\frac{3}{2}\right) $$
Plot the given point in a rectangular coordinate system. $$ \left(-\frac{5}{2}, \frac{3}{2}\right) $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{2}-2 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{2}+2 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x-2 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x+2 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=2 x+1 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=2 x-4 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-\frac{1}{2} x $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-\frac{1}{2} x+2 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=2|x| $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-2|x| $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=|x|+1 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=|x|-1 $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=9-x^{2} $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-x^{2} $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{3} $$
Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{3}-1 $$
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-5,5,1] \text { by }[-5,5,1]$$CAN'T COPY THE FIGURE
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-10,10,2] \text { by }[-4,4,2]$$CAN'T COPY THE FIGURE
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-20,80,10] \text { by }[-30,70,10]$$CAN'T COPY THE FIGURE
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-40,40,20] \text { by }[-1000,1000,100]$$CAN'T COPY THE FIGURE
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. $y={2}-1-2 x$
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. $y={1}-2-x$
Does the graph of $Y_{2}$ pass through the origin?
Does the graph of $Y_{1}$ pass through the origin?
At which point does the graph of $Y_{2}$ cross the $x$ -axis?
At which point does the graph of $Y_{2}$ cross the $y$ -axis?
At which points do the graphs of $Y_{1}$ and $Y_{2}$ intersect?
For which values of $x$ is $Y_{1}=Y_{2} ?$
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.CAN'T COPY THE GRAPH
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.$$y=-\frac{1}{x}\left(\text { Let } x=-2,-1,-\frac{1}{2},-\frac{1}{3}, \frac{1}{3}, \frac{1}{2}, 1, \text { and } 2 .\right)$$
The graphs show the percentage of high school seniors who used alcohol or marijuana during the 30 days prior to being surveyed for the University of Michigan's Monitoring the Future study.CAN'T COPY THE GRAPHa. Use the appropriate line graph to determine the percentage of seniors who used marijuana in 2005 .b. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2005 .$ Does the formula underestimate or overestimate the actual percentage displayed by the graph? By how much?c. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in 2005 .d. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2005 .$ How does this compare with your estimate in part (c)?e. For the period from 1980 through $2009,$ in which year was marijuana use by seniors at a minimum? Estimate the percentage of seniors who used marijuana in that year.
The graphs show the percentage of high school seniors who used alcohol or marijuana during the 30 days prior to being surveyed for the University of Michigan's Monitoring the Future study.CAN'T COPY THE GRAPHa. Use the appropriate line graph to determine the percentage of seniors who used alcohol in 2000 .b. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2000 .$ Does the formula underestimate or overestimate the actual percentage displayed by the graph? By how much?c. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in 2000 .d. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2000 .$ How does this compare with your estimate in part (c)?e. For the period from 1980 through $2009,$ in which year was alcohol use by seniors at a maximum? Estimate the percentage of seniors who 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 $57-60$.CAN'T COPY THE GRAPHAt 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 $57-60$.CAN'T COPY THE GRAPHAt 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 $57-60$.CAN'T COPY THE GRAPHEstimate, to the nearest tenth, the difference between the average number of awakenings during the night for 25 -yearold 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 $57-60$.CAN'T COPY THE GRAPHEstimate, to the nearest tenth, the difference between the average number of awakenings during the night for 18 -yearold men and 18 -year-old women.
What is the rectangular coordinate system?
Explain how to plot a point in the rectangular coordinate system. Give an example with your explanation.
Explain why $(5,-2)$ and $(-2,5)$ do not represent the same point.CAN'T COPY THE GRAPH
Explain how to graph an equation in the rectangular coordinate system.
What does a $[-20,2,1]$ by $[-4,5,0.5]$ viewing rectangle mean?
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 is not displaying number; among the x- and y-axes.
Determine whether each statement makes sense or does not make sense, and explain your reasoning.There is something wrong with my graphing utility because is not displaying number; I used I used the ordered pairs and (-2,2) and (0,0)(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 points 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.$$x y>0$$
List the quadrant or quadrants satisfying each condition.$$\frac{y}{x}<0$$
List the quadrant or quadrants satisfying each condition.$$x^{3}>0 \text { and } y^{3}<0$$
List the quadrant or quadrants satisfying each condition.$$x^{3}<0 \text { and } y^{3}>0$$
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.
Match the story with the correct figure. The figures are labeled (a), (b), (c), and (d).The snow fell more and more softly.
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 stopped. After a short time, the snow started falling hard.CAN'T COPY THE GRAPH
Select the graph that best illustrates each story.An airplane flew from Miami to San Francisco.CAN'T COPY THE GRAPH
Select the graph that best illustrates each story.At noon, you begin to breathe in.CAN'T COPY THE GRAPH
Select the graph that best illustrates each story.Measurements are taken of a person's height from birth to age 100CAN'T COPY THE GRAPH
Select the graph that best illustrates each story.You 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.CAN'T COPY THE GRAPH
This 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?
This will help you prepare for the material covered in the next section.Multiply and simplify: $12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)$
This will help you prepare for the material covered in the next section.Multiply and simplify: $(x-3)\left(\frac{3}{x-3}+9\right)$