Chapter 1

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(4,1),(3,-5),(-2,3),(3,7)\\}$$

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(-5,-2)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$\frac{7}{3}(2 x-1)=\frac{1}{5} x+\frac{2}{5}(4-3 x)$$

Graph each line by hand. Give the \(x\) - and y-intercepts. $$2 x-3 y=6$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(0,5),(1,3),(0,-4)\\}$$

Solve each problem. Women against the Men The men's Olympic pole vaulting winning heights in meters during year \(x\) can be approximated by \(H(x)=\frac{1}{48} x-35.83,\) where \(1896 \leq x \leq 2008 .\) (Assume that \(x\) is a multiple of 4 because the Olympics occur every 4 years.) (a) Evaluate \(H(1920)\) and interpret the result. (b) In 2008 the women's Olympic winning height in the pole vault was about 5 meters. Determine the years when this height would have beaten or tied the men's winning heights.

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(-2,-4)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$0.1 x-0.05=-0.07 x$$

Graph each line by hand. Give the \(x\) - and y-intercepts. $$2 x+5 y=10$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\begin{array}{|c|c|c|c|c|} \hline x & 11 & 12 & 13 & 14 \\ \hline y & -6 & -6 & -7 & -6 \\ \hline \end{array}$$

Solve each problem. Holiday Shopping In \(2012,\) U.S. holiday sales were \(\$ 569\) billion, and in 2015 , they were \(\$ 626\) billion. (Source: National Retail Federation.) (a) Find a linear function \(S\) that models these data, where \(x\) is the year. (b) Interpret the slope of the graph of \(S\). (c) Predict the year that U.S. holiday sales might reach \(\$ 721\) billion.

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(2,-2)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$1.1 x-2.5=0.3(x-2)$$

Graph each line by hand. Give the \(x\) - and y-intercepts. $$4 x-3 y=9$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\begin{array}{|c|c|c|c|c|} \hline x & 1 & 1 & 1 & 1 \\ \hline y & 12 & 13 & 14 & 15 \\ \hline \end{array}$$

Solve each problem. Bicycle Safety\(\quad\) A survey found that \(76 \%\) of bicycle riders do not wear helmets. (Source: Opinion Research Corporation for Glaxo Wellcome, Inc.) (a) Write a linear function \(f\) that computes the number of people who do not wear helmets among \(x\) bicycle riders. (b) There are approximately 38.7 million riders of all ages who do not wear helmets. Write a linear equation whose solution gives the total number of bicycle riders. Find this number of riders.

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(3,-3)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$0.40 x+0.60(100-x)=0.45(100)$$

A line having an equation of the form \(y=k x\), where \(k\) is a real number, \(k \neq 0\), will always pass through the origin \((0,0) .\) To graph such an equation by hand, we can determine a second point and then join the origin and that second point with a straight line. Use this method to graph each line. $$y=3 x$$

Give the equation of the \(x\) -axis.

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y & \sqrt{2} & \sqrt{3} & \sqrt{5} & \sqrt{6} & \sqrt{7} \end{array}$$

do each of the following. (a) Express the cost \(C\) as a function of \(x,\) where \(x\) represents the number of items as described. (b) Express the revenue \(R\) as a function of \(x .\) (c) Determine analytically the value of \(x\) for which revenue equals cost. (d) Graph \(y_{1}=C(x)\) and \(y_{2}=R(x)\) on the same \(x y\) -axes and interpret the graphs. Stuffing Envelopes \(\quad\) A student stuffs envelopes for extra income during her spare time. Her initial cost to obtain the necessary information for the job was \(\$ 200.00 .\) Each envelope costs \(\$ 0.02,\) and she gets paid \(\$ 0.04\) per envelope stuffed. Let \(x\) represent the number of envelopes stuffed.

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(3,0)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$1.30 x+0.90(0.50-x)=1.00(50)$$

A line having an equation of the form \(y=k x\), where \(k\) is a real number, \(k \neq 0\), will always pass through the origin \((0,0) .\) To graph such an equation by hand, we can determine a second point and then join the origin and that second point with a straight line. Use this method to graph each line. $$y=-2 x$$

Give the equation of the \(y\) -axis.

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{16} \\ \hline y & 0 & -1 & -2 & -3 & -4 \end{array}$$

do each of the following. (a) Express the cost \(C\) as a function of \(x,\) where \(x\) represents the number of items as described. (b) Express the revenue \(R\) as a function of \(x .\) (c) Determine analytically the value of \(x\) for which revenue equals cost. (d) Graph \(y_{1}=C(x)\) and \(y_{2}=R(x)\) on the same \(x y\) -axes and interpret the graphs. Copier Service A technician runs a copying service in his home. He paid \(\$ 3500\) for the copier and a lifetime service contract. Each sheet of paper costs \(\$ 0.01,\) and he gets paid \(\$ 0.05\) per copy. Let \(x\) be the number of copies he makes.

Locate each point on a rectangular coordinate system. Identify the quadrant, if any, in which each point lies. $$(-2,0)$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$2[x-(4+2 x)+3]=2 x+2$$

A line having an equation of the form \(y=k x\), where \(k\) is a real number, \(k \neq 0\), will always pass through the origin \((0,0) .\) To graph such an equation by hand, we can determine a second point and then join the origin and that second point with a straight line. Use this method to graph each line. $$y=-0.75 x$$

Graph each linear function on a graphing calculator, using the two different windows given. State which window gives a comprehensive graph. \(f(x)=4 x+20\) Window A: \([-10,10]\) by \([-10,10]\) Window B: \([-10,10]\) by \([-5,25]\)

do each of the following. (a) Express the cost \(C\) as a function of \(x,\) where \(x\) represents the number of items as described. (b) Express the revenue \(R\) as a function of \(x .\) (c) Determine analytically the value of \(x\) for which revenue equals cost. (d) Graph \(y_{1}=C(x)\) and \(y_{2}=R(x)\) on the same \(x y\) -axes and interpret the graphs. Delivery Service \(A\) truck driver operates a delivery ervice. His start-up costs amounted to \(\$ 2300 .\) He estimates that it costs him (in terms of gasoline, wear and tear =on his truck, etc.) \(\$ 3.00\) per delivery. He charges \(\$ 5.50\) per delivery. Let \(x\) represent the number of deliveries he makes.

Name the possible quadrants in which the point ( \(x, y\) ) can lie if the given condition is true. (Hint: Consider the rules for determining the product and the quotient of signed numbers.) $$x y>0$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$6[x-(2-3 x)+1]=4 x-6$$

A line having an equation of the form \(y=k x\), where \(k\) is a real number, \(k \neq 0\), will always pass through the origin \((0,0) .\) To graph such an equation by hand, we can determine a second point and then join the origin and that second point with a straight line. Use this method to graph each line. $$y=1.5 x$$

Graph each linear function on a graphing calculator, using the two different windows given. State which window gives a comprehensive graph. \(f(x)=-5 x+30\) Window A: \([-10,10]\) by \([-10,40]\) Window B: \([-5,5]\) by \([-5,40]\)

do each of the following. (a) Express the cost \(C\) as a function of \(x,\) where \(x\) represents the number of items as described. (b) Express the revenue \(R\) as a function of \(x .\) (c) Determine analytically the value of \(x\) for which revenue equals cost. (d) Graph \(y_{1}=C(x)\) and \(y_{2}=R(x)\) on the same \(x y\) -axes and interpret the graphs. Baking and Selling Cakes A baker makes cakes and sells them at county fairs. Her initial cost for the Pointe Coupee parish fair was \(\$ 40.00 .\) She figures that each cake costs \(\$ 2.50\) to make, and she charges \(\$ 6.50\) per cake. Let \(x\) represent the number of cakes sold. (Assume that there were no cakes left over.)

Name the possible quadrants in which the point ( \(x, y\) ) can lie if the given condition is true. (Hint: Consider the rules for determining the product and the quotient of signed numbers.) $$x y<0$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$\frac{5}{6} x-2 x+\frac{1}{3}=\frac{1}{3}$$

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &5 x+3 y=15\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

Graph each linear function on a graphing calculator, using the two different windows given. State which window gives a comprehensive graph. \(f(x)=3 x+10\) Window A: \([-3,3]\) by \([-5,5]\) Window B: \([-5,5]\) by \([-10,14]\)

find the constant of variation \(k\) and the undetermined value in the table if \(y\) is directly proportional to \(x\). $$\begin{array}{|c|c|c|c|c|} \hline x & 3 & 5 & 6 & 8 \\ \hline y & 7.5 & 12.5 & 15 & ? \end{array}$$

Name the possible quadrants in which the point ( \(x, y\) ) can lie if the given condition is true. (Hint: Consider the rules for determining the product and the quotient of signed numbers.) $$\frac{x}{y}<0$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$\frac{3}{4}+\frac{1}{5} x-\frac{1}{2}=\frac{4}{5} x$$

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &6 x+5 y=9\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

Graph each linear function on a graphing calculator, using the two different windows given. State which window gives a comprehensive graph. \(f(x)=-6\) Window A: \([-5,5]\) by \([-5,5]\) Window B: \([-10,10]\) by \([-10,10]\)

find the constant of variation \(k\) and the undetermined value in the table if \(y\) is directly proportional to \(x\). $$\begin{array}{|c|c|c|c|c|} \hline x & 1.2 & 4.3 & 5.7 & ? \\ \hline y & 3.96 & 14.19 & 18.81 & 23.43 \end{array}$$

Name the possible quadrants in which the point ( \(x, y\) ) can lie if the given condition is true. (Hint: Consider the rules for determining the product and the quotient of signed numbers.) $$\frac{x}{y}>0$$

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$5 x-(8-x)=2[-4-(3+5 x-13)]$$