Chapter 1

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. $$\text { Through }(-2,-3), m=-\frac{3}{4}$$

Solve each formula for the specified variable. \(S=\frac{n}{2}\left[2 a_{1}+(n-1) d\right]\) for \(a_{1} \quad\) (Mathematics)

Solve each equation and inequality analytically. Use interval notation to write the solution set for each inequality. (a) \(1-2 x=0\) (b) \(1-2 x \leq 0\) (c) \(1-2 x \geq 0\)

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. $$\text { Through }(-1,4), m=0$$

Solve each formula for the specified variable. \(s=\frac{1}{2} g t^{2}\) for \(g \quad\) (Distance traveled by a falling object)

The following table lists the U.S. total revenue generated in 2016 in billions of dollars for various companies. $$\begin{array}{l|c}\hline \text { Company } & \text { Revenue } \\\\\hline \text { Apple } & 216 \\\\\text { Alphabet } & 90 \\\\\text { Google } & 89 \\\\\text { Microsoft } & 85\end{array}$$ (a) Using ordered pairs, write a function \(A\) that gives the revenue for each company in billions of dollars. Interpret the first ordered pair. (b) Repeat part (a) using a diagram. (c) Identify the domain and range of \(A\).

Solve each equation and inequality analytically. Use interval notation to write the solution set for each inequality. (a) \(4-3 x=0\) (b) \(4-3 x \leq 0\) (c) \(4-3 x \geq 0\)

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. Through \(\left(\frac{9}{4}, 2\right),\) undefined slope

Solve each formula for the specified variable. \(A=\frac{24 f}{B(p+1)}\) for \(p \quad\) (Approximate annual interest rate)

Solve each equation and inequality analytically. Use interval notation to write the solution set for each inequality. (a) \(x+12=4 x\) (b) \(x+12>4 x\) (c) \(x+12<4 x\)

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. $$\text { Through }(0,-4), m=\frac{3}{4}$$

The function \(f\) gives the number \(y\) in thousands of radio stations on the air during year \(x .\) $$\begin{aligned}f=&\\{(1990,10.8),(2000,12.8),(2005,13.5)\\\&(2012,15.1),(2015,16.4)\\}\end{aligned}$$ (Source: M. Street Corporation.) (a) Use a mapping diagram (see HGURE 21) to represent \(f\). (b) Evaluate \(f(2000)\) and explain what it means. (c) Identify the domain and range of \(f\)

Solve each equation and inequality analytically. Use interval notation to write the solution set for each inequality. (a) \(5-3 x=x+1\) (b) \(5-3 x \leq x+1\) (c) \(5-3 x \geq x+1\)

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. $$\text { Through }(0,5), m=-2.5$$

The function \(f\) gives the number \(y\) in billions of dollars of personal health care expenditures during year \(x .\) $$\begin{array}{r}f=\\{(2010,2195),(2011,2273),(2012,2366) \\\\(2013,2436),(2014,2563),(2015,2717)\\}\end{array}$$ (Source: U.S. Center for Medicare and Medicaid Services.) (a) Use a mapping diagram to represent \(f\) (b) Evaluate \(f(2012)\) and explain what it means. (c) Identify the domain and range of \(f .\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(9-(x+1)<0\) (b) \(9-(x+1) \geq 0\)

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. Through \((-3,0),\) undefined slope

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(6+3(1-x) \geq 0\) (b) \(6+3(1-x)<0\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(2 x-3>x+2\) (b) \(2 x-3 \leq x+2\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(5-3 x \leq-11+x\) (b) \(5-3 x>-11+x\)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(10 x+5-7 x \geq 8(x+2)+4\) (b) \(10 x+5-7 x<8(x+2)+4\)

By noon, 3 inches of rain had fallen during a storm. Rain continued to fall at a rate of \(\frac{1}{4}\) inch per hour. (a) Find a formula for a linear function \(f\) that models the amount of rainfall \(x\) hours past noon. (b) Find the total amount of rainfall by 2: 30 P.M.

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(6 x+2+10 x>-2(2 x+4)+10\) (b) \(6 x+2+10 x \leq-2(2 x+4)+10\)

When the relative humidity is \(100 \%\) air cools \(5.8^{\circ} \mathrm{F}\) for every 1 -mile increase in altitude. If the temperature is \(80^{\circ} \mathrm{F}\) on the ground, then \(f(x)=80-5.8 x\) calculates the air temperature \(x\) miles above the ground. Find \(f(3)\) and interpret the result. (Source: Battan, \(L\). Weather in Your Life, W.H. Freeman.)

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(x+2(-x+4)-3(x+5)<-4\) (b) \(x+2(-x+4)-3(x+5) \geq-4\)

When a bolt of lightning strikes in the distance, there is often a delay between seeing the lightning and hearing the thunder. The function \(f(x)=\frac{x}{5}\) computes the approximate distance in miles between an observer and a bolt of lightning when the delay is \(x\) seconds. (a) Find \(f(15)\) and interpret the result. (b) Graph \(y=f(x) .\) Let the domain of \(f\) be \([0,20]\).

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(5,7), Q(2,11)$$

Solve each inequality analytically, writing the solution set in interval notation. Support your answer graphically. (Hint: Once part (a) is done, the answer to part (b) follows.) (a) \(-11 x-(6 x-4)+5-3 x \leq 1\) (b) \(-11 x-(6 x-4)+5-3 x>1\)

Function \(f\) gives the median 2015 weekly income (in dollars) by educational attainment for people 25 years old and over. This function is defined by \(f(N)=493, f(H)=678, f(B)=1137\) and \(f(M)=1341,\) where \(N\) denotes no high school diploma, \(H\) a high school diploma, \(B\) a bachelor's degree, and \(M\) a master's degree. (Source: U.S. Bureau of Labor Statistics.) (a) Write \(f\) as a set of ordered pairs. (b) Give the domain and range of \(f\). (c) Discuss the relationship between education and income.

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(-2,5), Q(4,-3)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$\frac{1}{3} x-\frac{1}{5} x \leq 2$$

If the sales tax rate is \(7.5 \%,\) write a function \(f\) that calculates the sales tax on a purchase of \(x\) dollars. What is the sales tax on a purchase of \(\$ 86 ?\)

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(-8,-2), Q(-3,-5)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$\frac{3 x}{2}+\frac{4 x}{7} \geq-5$$

If college tuition costs \(\$ 192\) per credit and fees are fixed at \(\$ 275,\) write a formula for a function \(f\) that calculates the tuition and fees for taking \(x\) credits. What is the total cost of taking 11 credits?

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(-6,-10), Q(6,5)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$\frac{x-2}{2}-\frac{x+6}{3}>-4$$

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(9.2,3.4), Q(6.2,7.4)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$\frac{2 x+3}{5}-\frac{3 x-1}{2}<\frac{4 x+7}{2}$$

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(8.9,1.6), Q(3.9,13.6)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$0.6 x-2(0.5 x+0.2) \leq 0.4-0.3 x$$

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(13 x,-23 x), Q(6 x, x), x>0$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$-0.9 x-(0.5+0.1 x)>-0.3 x-0.5$$

Find (a) the distance between \(P\) and \(Q\) and (b) the coordinates of the midpoint \(M\) of the segment joining \(P\) and \(Q\). $$P(12 y,-3 y), Q(20 y, 12 y), y>0$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$-\frac{1}{2} x+0.7 x-5>0$$

Suppose that \(P\) is an endpoint of a segment \(P Q\) and \(M\) is the midpoint of \(P Q .\) Find the coordinates of endpoint \(Q\). $$P(7,-4), M(8,5)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$\frac{3}{4} x-0.2 x-6 \leq 0$$

Suppose that \(P\) is an endpoint of a segment \(P Q\) and \(M\) is the midpoint of \(P Q .\) Find the coordinates of endpoint \(Q\). $$P(13,5), M(-2,-4)$$

Solve each inequality analytically. Write the solution set in interval notation. Support the answer graphically. $$-4(3 x+2) \geq-2(6 x+1)$$

Suppose that \(P\) is an endpoint of a segment \(P Q\) and \(M\) is the midpoint of \(P Q .\) Find the coordinates of endpoint \(Q\). $$P(5.64,8.21), M(-4.04,1.60)$$