Chapter 1

In Exercises 17–30, write an equation for each line described. Passes through \((-8,0)\) and \((-1,3)\)

Graph the following equations and explain why they are not graphs of functions of \(x .\) a. \(|y|=x \quad\) b. \(y^{2}=x^{2}\)

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=x^{3} \quad \text { Left } 1, \text { down } 1 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ f(x)=\frac{x-1}{x^{2}-x-6} $$

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ f(x)=x^{2}+1 $$

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ |t-1| \leq 3 $$

In Exercises 17–30, write an equation for each line described. Has slope \(-5 / 4\) and \(y\) -intercept 6

Graph the following equations and explain why they are not graphs of functions of \(x .\) a. \(|x|+|y|=1 \quad\) b. \(|x+y|=1\)

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=x^{2 / 3} \quad \text { Right } 1, \text { down } 1 $$

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ f(x)=x^{2}+x $$

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ |t+2|<1 $$

In Exercises 17–30, write an equation for each line described. Has slope 1\(/ 2\) and \(y\) -intercept \(-3\)

Graph the functions in Exercises \(23-26\) $$ f(x)=\left\\{\begin{array}{ll}{x,} & {0 \leq x \leq 1} \\ {2-x,} & {1

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ g(x)=x^{3}+x $$

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ |3 y-7|<4 $$

In Exercises 17–30, write an equation for each line described. Passes through \((-12,-9)\) and has slope 0

Graph the functions in Exercises \(23-26\) $$ g(x)=\left\\{\begin{array}{ll}{1-x,} & {0 \leq x \leq 1} \\ {2-x,} & {1

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=-\sqrt{x} \quad \text { Right } 3 $$

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ g(x)=x^{4}+3 x^{2}-1 $$

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ |2 y+5|<1 $$

In Exercises 17–30, write an equation for each line described. Passes through \((1 / 3,4),\) and has no slope

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=2 x-7 \quad \text { Up } 7 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=\sin 250 x $$

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ g(x)=\frac{1}{x^{2}-1} $$

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ \left|\frac{z}{5}-1\right| \leq 1 $$

In Exercises 17–30, write an equation for each line described. Has \(y\) -intercept 4 and \(x\) -intercept \(-1\)

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=\frac{1}{2}(x+1)+5 \quad \text { Down } 5, \text { right } 1 $$

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ g(x)=\frac{x}{x^{2}-1} $$

In Exercises 17–30, write an equation for each line described. Has \(y\) -intercept \(-6\) and \(x\) -intercept 2

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ \left|\frac{3}{2} z-1\right| \leq 2 $$

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=1 / x \quad \text { Up } 1, \text { right } 1 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=\cos \left(\frac{x}{50}\right) $$

a. Graph \(y=\cos x\) and \(y=\sec x\) together for \(-3 \pi / 2 \leq x\) \(\leq 3 \pi / 2\) . Comment on the behavior of sec \(x\) in relation to the signs and values of \(\cos x\) b. Graph \(y=\sin x\) and \(y=\csc x\) together for \(-\pi \leq x \leq 2 \pi\) Comment on the behavior of \(\csc x\) in relation to the signs and values of \(\sin x .\)

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=\frac{1}{t-1} $$

In Exercises 17–30, write an equation for each line described. Passes through \((5,-1)\) and is parallel to the line \(2 x+5 y=15\)

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ \left|3-\frac{1}{x}\right|<\frac{1}{2} $$

Exercises \(19-28\) tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. $$ y=1 / x^{2} \quad \text { Left } 2, \text { down } 1 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=\frac{1}{10} \sin \left(\frac{x}{10}\right) $$

Graph \(y=\tan x\) and \(y=\cot x\) together for \(-7 \leq x \leq 7 .\) Comment on the behavior of \(\cot x\) in relation to the signs and values of \(\tan x .\)

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=\left|t^{3}\right| $$

In Exercises 17–30, write an equation for each line described. Passes through \((-\sqrt{2}, 2)\) parallel to the line \(\sqrt{2} x+5 y=\sqrt{3}\)

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ \left|\frac{2}{x}-4\right|<3 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=x+\frac{1}{10} \sin 30 x $$

Graph \(y=\sin x\) and \(y=\lfloor\sin x\rfloor\) together. What are the domain and range of \(|\sin x| ?\)

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=2 t+1 $$

In Exercises 17–30, write an equation for each line described. Passes through \((4,10)\) and is perpendicular to the line \(6 x-3 y=5\)

Solve the inequalities in Exercises \(19-34,\) expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. $$ |2 s| \geq 4 $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=x^{2}+\frac{1}{50} \cos 100 x $$

Graph \(y=\sin x\) and \(y=\lceil\sin x\rceil\) together. What are the domain and range of \(\lceil\sin x\rceil\) ?

In Exercises \(19-30,\) say whether the function is even, odd, or neither. Give reasons for your answer. $$ h(t)=2|t|+1 $$