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.$$[-5,5,1] \text { by }[-5,5,1]$$(FIGURE CANNOT COPY)
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-10,10,2] \text { by }[-4,4,2]$$(FIGURE CANNOT COPY)
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-20,80,10] \text { by }[-30,70,10]$$(FIGURE CANNOT COPY)
Match the viewing rectangle with the correct figure. Then label the tick marks in the figure to illustrate this viewing rectangle.$$[-40,40,20] \text { by }[-1000,1000,100]$$(FIGURE CANNOT COPY)
The table of values was generated by a graphing utilitywith a TABLE feature. Use the table to solve.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. $y_{2}=1-2 x$(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.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. $y_{1}=2-x$(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.Does the graph of $Y_{1}$ pass through the origin?(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.At which point does the graph of $Y_{2}$ cross the $x$ -axis?(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.At which point does the graph of $Y_{2}$ cross the $y$ -axis?(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.At which points do the graphs of $Y_{1}$ and $Y_{2}$ intersect?(TABLE CANNOT COPY)
The table of values was generated by a graphing utility with a TABLE feature. Use the table to solve.For which values of $x$ is $Y_{1}=Y_{2} ?$(TABLE CANNOT COPY)
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.(GRAPH CANNOT COPY)
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 had ever used alcohol or marijuana.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.(GRAPH CANNOT COPY)
The graphs show the percentage of high school seniors who had ever used alcohol or marijuana.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 .(GRAPH CANNOT COPY)
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.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?(GRAPH CANNOT COPY)
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.At which age do men have the greatest number of awakenings during the night? What is the average number of awakenings at that age?(GRAPH CANNOT COPY)
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.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.(GRAPH CANNOT COPY)
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.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.(GRAPH CANNOT COPY)
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.
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?
Use a graphing utility to verify each of your hand-drawn graphs. 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..(GRAPH CANNOT COPY)
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.$$x y>0$$
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.(FIGURE CANNOT COPY)
Match the story with the correct figure. The figures are labeled$(a),(b),(c),$ and $(d)$The snow fell more and more softly.(FIGURE CANNOT COPY)
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.(FIGURE CANNOT COPY)
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.(FIGUbRE CANNOT COPY)
Select the graph that best illustrates each story.An airplane flew from Miami to San Francisco.(GRAPH CANNOT COPY)
Select the graph that best illustrates each story.At noon, you begin to breathe in.(GRAPH CANNOT COPY)
Select the graph that best illustrates each story.Measurements are taken of a person's height from birth to age 100(GRAPH CANNOT COPY)
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.(GRAPH CANNOT COPY)
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: $(x-3)\left(\frac{3}{x-3}+9\right)$