Chapter 2

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=|x+2|$$

Use a graphing calculator in dot mode with window \([-5,5]\) by \([-3,3]\) to graph each equation. (Refer to your descriptions in Exercises 41-44.) $$y=-[x]$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & 10 \\ -2 & 5 \\ -1 & 2 \\ 0 & 1 \\ 1 & 2 \\ 2 & 5 \\ 3 & 10 \end{array}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=(x-1)^{3}$$

Solve each equation or inequality. $$|2 x+4|+2=10$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & 16 \\ -2 & 5 \\ -1 & 1 \\ 0 & -4 \\ 1 & 1 \\ 2 & 5 \\ 3 & 16 \end{array}$$

Use transformations of graphs to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$f(x)=2+\sqrt{-(x-3)}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=|x|-3$$

Solve each equation or inequality. $$3|4-3 x|-4=8$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & 10 \\ -2 & 5 \\ -1 & 2 \\ 0 & 0 \\ 1 & -2 \\ 2 & -5 \\ 3 & -10 \end{array}$$

Use transformations of graphs to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$f(x)=(x-1)^{3}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=\sqrt{x-2}-1$$

Solve each equation or inequality. $$5|x+3|-2=18$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & -5 \\ -2 & -4 \\ -1 & -1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ 3 & 5 \end{array}$$

Use transformations of graphs to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$f(x)=(x+2)^{3}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=\sqrt{x+3}-4$$

Tables for functions \(f\) and \(g\) are given. Evaluate each expression, if possible. (a) \((g \circ f)(1)\) (b) \((f \circ g)(4)\) (c) \((f \circ f)(3)\) $$\begin{array}{c|cc|c}\boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) \\\\\hline 1 & 4 & 1 & 2 \\\\\hline 2 & 3 & 2 & 3 \\\\\hline 3 & 1 & 3 & 4 \\\\\hline 4 & 2 & 4 & 5 \end{array}$$

Postage Rates In 2013 , the retail flat rate in dollars for first-class mail weighing up to 5 ounces could be computed by the piecewise constant function \(f,\) where \(x\) is the number of ounces. $$f(x)=\left\\{\begin{array}{ll} 0.92 & \text { if } 0

Solve each equation or inequality. $$\frac{1}{2}\left|-2 x+\frac{1}{2}\right|=\frac{3}{4}$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & 5 \\ -2 & 4 \\ -1 & 3 \\ 0 & 2 \\ 1 & 1 \\ 2 & 0 \\ 3 & -1 \end{array}$$

Use transformations of graphs to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$f(x)=-x^{3}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=(x+2)^{2}+3$$

Super Bowl Ad cost The average cost of a 30 -second Super Bowl ad in millions of dollars is approximated by the piecewise-defined function $$f(x)=\left\\{\begin{array}{ll} 0.0475 x-93.3 & \text { if } 1967 \leq x \leq 1998 \\ 0.1333 x-264.7284 & \text { if } 1998

Solve each equation or inequality. $$|3(x-5)+2|+3=9$$

Based on the ordered pairs seen in each table, make a conjecture about whether the function \(f\) is even, odd, or neither even nor odd. $$\begin{array}{r|r} x & f(x) \\ \hline-3 & -1 \\ -2 & 0 \\ -1 & 1 \\ 0 & 2 \\ 1 & 3 \\ 2 & 4 \\ 3 & 5 \end{array}$$

Use transformations of graphs to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$f(x)=(-x)^{3}+1$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=(x-4)^{2}-4$$

Solve each equation or inequality. $$4.2|0.5-x|+1=3.1$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=x^{4}-7 x^{2}+6$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=|x+4|-2$$

Solve each equation or inequality. $$|3 x-1|<8$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=-2 x^{6}-8 x^{2}$$

Use translations of one of the basic functions \(y=x^{2}, y=x^{3},\) \(y=\sqrt{x},\) or \(y=|x|\) to sketch a graph of \(y=f(x)\) by hand. Do not use a calculator. $$y=(x+3)^{3}-1$$

The graphing calculator screen on the left shows three functions: \(\mathrm{Y}_{1}, \mathrm{Y}_{2},\) and \(\mathrm{Y}_{3} .\) The last of these, \(\mathrm{Y}_{3}\), is defined as \(\mathrm{Y}_{1} \circ \mathrm{Y}_{2},\) indicated by the notation \(\mathrm{Y}_{3}=\mathrm{Y}_{1}\left(\mathrm{Y}_{2}\right) .\) The table on the right shows selected values of \(\mathbf{X},\) along with the calculated values of \(\mathbf{Y}_{3} .\) Predict the display for \(\mathbf{Y}_{3}\) for the given value of \(\mathbf{X}\). $$\mathbf{X}=-1$$

Solve each equation or inequality. $$|15-x|<7$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=3 x^{3}-x$$

Solve each equation or inequality. $$|7-4 x| \leq 11$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=-x^{5}+2 x^{3}-3 x$$

Cellular Phone Bills Suppose that the charges for an international cellular phone call are \(\$ 0.50\) for the first minute and \(\$ 0.25\) for each additional minute. Assume that a fraction of a minute is rounded up. A. Determine the cost of a phone call lasting 3.5 minutes. B. Find a formula for a function \(f\) that computes the cost of a telephone call \(x\) minutes long, where \(0

Solve each equation or inequality. $$|2 x-3|>1$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=x^{6}-4 x^{4}+5$$

Lumber costs Lumber that is used to frame walls of houses is frequently sold in lengths that are multiples of 2 feet. If the length of a board is not exactly a multiple of 2 feet, there is often no charge for the additional length. For example, if a board measures at least 8 feet, but less than 10 feet, then the consumer is charged for only 8 feet. Lumber costs Lumber that is used to frame walls of houses is frequently sold in lengths that are multiples of 2 feet. If the length of a board is not exactly a multiple of 2 feet, there is often no charge for the additional length. For example, if a board measures at least 8 feet, but less than 10 feet, then the consumer is charged for only 8 feet. A. Suppose that the cost of lumber is \(\$ 0.80\) every 2 feet. Find a formula for a function \(f\) that computes the cost of a board \(x\) feet long for \(6 \leq x \leq 18\) B. Use a graphing calculator to graph \(f\) C. Determine the costs of boards with lengths of 8.5 feet and 15.2 feet.

Solve each equation or inequality. $$|4-3 x|>1$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=8$$

Each figure shows the graph of \(y=f(x)\). Sketch by hand the graphs of the functions in parts (a), (b), and (c), and answer the question in part (d). (a) \(y=f(2 x) \quad\) (b) \(y=f(-x) \quad\) (c) \(y=3 f(x)\) (d) What symmetry does the graph of \(y=f(x)\) exhibit?

Use \(f(x)\) and \(g(x)\) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) \((f \circ g)(x) \quad\) (b) \((g \circ f)(x) \quad\) (c) \((f \circ f)(x)\). $$f(x)=x^{3}, \quad g(x)=x^{2}+3 x-1$$

An express-mail company charges \(\$ 25\) for a package weighing up to 2 pounds. For each additional pound or fraction of a pound, there is an additional charge of \(\$ 3 .\) Let \(D(x)\) represent the cost to send a package weighing \(x\) pounds. Graph \(y=D(x)\) for \(x\) in the interval \((0,6]\)

Solve each equation or inequality. $$|-3 x+8| \geq 3$$

Each function is either even or odd. Use \(f(-x)\) to state which situation applies. $$f(x)=3 x^{5}-x^{3}+7 x$$

Use \(f(x)\) and \(g(x)\) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) \((f \circ g)(x) \quad\) (b) \((g \circ f)(x) \quad\) (c) \((f \circ f)(x)\). $$f(x)=2-x, \quad g(x)=\frac{1}{x^{2}}$$