Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(|-59.34|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(|5-\pi|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(|\pi-7|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(\sqrt{(-3)^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. ln(1)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. e0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \((\sqrt[3]{3})^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(\sqrt[3]{(-15)^{3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(\sqrt[3]{-8^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, evaluate the expression without using a calculator. \(|1-\pi|-\pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, each graph is a slight variation on the graph of one of the twelve basic functions described in this section. Match the graph to one of the twelve functions (a)(l) and then support your answer by checking the graph on your calculator. (All graphs are shown in the window [-4.7, 4.7]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The function whose domain excludes zero

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The function whose domain consists of all nonnegative real numbers

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The two functions that have at least one point of discontinuity

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The function that is not a continuous function

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The six functions that are bounded below

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-18, identify which of Exercises 1-12 display functions that fit the description given. The four functions that are bounded above

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The four functions that are odd

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The six functions that are increasing on their entire domains

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The three functions that are decreasing on the interval (- \(\infty\), 0)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The three functions with infinitely many local extrema

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The three functions with no zeros

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The three functions with range {all real numbers}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The four functions that do not have end behavior \(\lim _{x \rightarrow+\infty} f(x)=+\infty\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The three functions with end behavior \(\lim _{x \rightarrow-\infty} f(x)=-\infty\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The four functions whose graphs look the same when turned upside-down and flipped about the y-axis

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-28, identify which of the twelve basic functions fit the description given. The two functions whose graphs are identical except for a horizontal shift

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(f(x)=x^{2}-5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(g(x)=|x-4|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(h(x)=\ln (x+6)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(k(x)=1 / x+3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(s(x)=\operatorname{int}(x / 2)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29-34, use your graphing calculator to produce a graph of the function. Then determine the domain and range of the function by looking at its graph. \(p(x)=(x+3)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35-42, graph the function. Then answer the following questions: (a) On what interval, if any, is the function increasing? Decreasing? (b) Is the function odd, even, or neither? (c) Give the functions extrema, if any. (d) How does the graph relate to a graph of one of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find the horizontal asymptotes for the graph shown in Exercise 11.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find the horizontal asymptotes for the graph of (x) in Exercise 37.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(f(x)=\left\{\begin{array}{ll}x & \text { if } x \leq 0 \\x^{2} & \text { if } x>0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(g(x)=\left\{\begin{array}{ll}x^{3} & \text { if } x \leq 0 \\e^{x} & \text { if } x>0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(h(x)=\left\{\begin{array}{ll}|x| & \text { if } x<0 \\\sin x & \text { if } x \geq 0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(w(x)=\left\{\begin{array}{ll}1 / x & \text { if } x<0 \\\sqrt{x} & \text { if } x \geq 0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(f(x)=\left\{\begin{array}{ll}\cos x & \text { if } x \leq 0 \\e^{x} & \text { if } x>0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(g(x)=\left\{\begin{array}{ll}|x| & \text { if } x<0 \\x^{2} & \text { if } x \geq 0\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(f(x)=\left\{\begin{array}{ll}-3-x & \text { if } x \leq 0 \\1 & \text { if } 0<x<1 \\x^{2} & \text { if } x \geq 1\end{array}\right.\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 45-52, sketch the graph of the piecewise-defined function. (Try doing it without a calculator.) In each case, give any points of discontinuity. \(f(x)=\left\{\begin{array}{ll}x^{2} & \text { if } x<-1 \\|x| & \text { if }-1 \leq x<1 \\\text { int }(x) & \text { if } x \geq 1\end{arra

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The function \(f(x)=\sqrt{x^{2}}\) is one of our twelve basic functions written in another form. (a) Graph the function and identify which basic function it is. (b) Explain algebraically why the two functions are equal.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The function \(g(x)=\sqrt{x^{2}+0.0001}-0.01\) is not one of our twelve basic functions written in another form. (a) Graph the function and identify which basic function it appears to be. (b) Verify numerically that it is not the basic function that it appears to be.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The function f(x) = ln(ex) is one of our twelve basic functions written in another form. (a) Graph the function and identify which basic function it is. (b) Explain how the equivalence of the two functions in (a) shows that the natural logarithm function is not bounded above (even though it

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Let f(x) be the function that gives the cost, in cents, to mail a first-class package that weighs x ounces. In August of 2009, the cost was $1.22 for a package that weighed up to 1 ounce, plus 17 cents for each additional ounce or portion thereof (up to 13 ounces). (Source: United States Postal Servi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Set your calculator to DOT mode and graph the greatest integer function, y = int(x), in the window [-4.7, 4.7] by [-3.1, 3.1] . Then complete the following analysis.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The greatest integer function has an inverse function. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The logistic function has two horizontal asymptotes. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which function has range {all real numbers}? (A) \(f(x)=4+\ln x\) (B) \(f(x)=3-1 / x\) (C) \(f(x)=5 /\left(1+e^{-x}\right)\) (D) \(f(x)=\operatorname{int}(x-2)\) (E) \(f(x)=4 \cos x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which function is bounded both above and below? (A) \(f(x)=x^{2}-4\) (B) \(f(x)=(x-3)^{3}\) (C) \(f(x)=3 e^{x}\) (D) \(f(x)=3+1 /\left(1+e^{-x}\right)\) (E) \(f(x)=4-|x|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following is the same as the restricted-domain function \(f(x)=\text { int }(x), 0 \leq x<2 \text { ? }\) (A) \(f(x)=\left\{\begin{array}{ll}0 & \text { if } 0 \leq x<1 \\1 & \text { if } x=1 \\2 & \text { if } 1<x<2\end{array}\right.\) (B) \(f(x)=\left\{\begin{array}{ll}0 & \t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which function is increasing on the interval \((-\infty, \infty)\)? (A) \(f(x)=\sqrt{3+x}\) (B) \(f(x)=\operatorname{int}(x)\) (C) \(f(x)=2 x^{2}\) (D) \(f(x)=\sin x\) (E) \(f(x)=3 /\left(1+e^{-x}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
For positive values of x, we wish to compare the values of the basic functions x2, x, and \(\sqrt(x)\) (a) How would you order them from least to greatest? (b) Graph the three functions in the viewing window [0, 30] by [0, 20]. Does the graph confirm your response in (a)? (c) Now graph th

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Odds and Evens There are four odd functions and three even functions in the gallery of twelve basic functions. After multiplying these functions together pairwise in different combinations and exploring the graphs of the products, make a conjecture about the symmetry of: (a) a product of two odd

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Assign to each student in the class the name of one of the twelve basic functions, but secretly so that no student knows the name of another. (The same function name could be given to several students, but all the functions should be used at least once.) Let each student make a one sen

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Pepperoni Pizzas For a statistics project, a student counted the number of pepperoni slices on pizzas of various sizes at a local pizzeria, compiling the following table: (a) Explain why the pepperoni count (P) ought to be proportional to the square of the radius (r). (b) Assuming t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Inverse Functions Two functions are said to be inverses of each other if the graph of one can be obtained from the graph of the other by reflecting it across the line . For example, the functions with the graphs shown below are inverses of each other: (a) Two of the twelve basic functions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Identifying a Function by Its Properties (a) Seven of the twelve basic functions have the property that f(0) = 0. Which five do not? (b) Only one of the twelve basic functions has the property that \(f(x+y)=f(x)+f(y)\) for all x and y in its domain. Which one is it? (c) One of the twel