Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. x=3 y-6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. x=0.5 y+1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=y^{2}+4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=y^{2}-6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\frac{y-2}{y+3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\frac{3 y-1}{y+2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\frac{2 y+1}{y-4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\frac{4 y+3}{3 y-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\sqrt{y+3}, y \geq-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, solve the equation for y. \(x=\sqrt{y-2}, y \geq 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the (x, y) pair for the value of the parameter \(x=3 t \text { and } y=t^{2}+5 \text { for } t=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the (x, y) pair for the value of the parameter \(x=5 t-7 \text { and } y=17-3 t \text { for } t=-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the (x, y) pair for the value of the parameter \(x=t^{3}-4 t \text { and } y=\sqrt{t+1} \text { for } t=3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find the (x, y) pair for the value of the parameter \(x=|t+3| \text { and } y=1 / t \text { for } t=-8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, complete the following. (a) Find the points determined by t = -3, -2, -1, 0, 1, 2, and 3. (b) Find a direct algebraic relationship between x and y and determine whether the parametric equations determine y as a function of x. (c) Graph the relationship in the xy-plane. \(x=2 t \

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, complete the following. (a) Find the points determined by t = -3, -2, -1, 0, 1, 2, and 3. (b) Find a direct algebraic relationship between x and y and determine whether the parametric equations determine y as a function of x. (c) Graph the relationship in the xy-plane. \(x=t+1 \

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, complete the following. (a) Find the points determined by t = -3, -2, -1, 0, 1, 2, and 3. (b) Find a direct algebraic relationship between x and y and determine whether the parametric equations determine y as a function of x. (c) Graph the relationship in the xy-plane. \(x=t^{2}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, complete the following. (a) Find the points determined by t = -3, -2, -1, 0, 1, 2, and 3. (b) Find a direct algebraic relationship between x and y and determine whether the parametric equations determine y as a function of x. (c) Graph the relationship in the xy-plane. \(x=\sqrt

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9-12, the graph of a relation is shown. (a) Is the relation a function? (b) Does the relation have an inverse that is a function?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9-12, the graph of a relation is shown. (a) Is the relation a function? (b) Does the relation have an inverse that is a function?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9-12, the graph of a relation is shown. (a) Is the relation a function? (b) Does the relation have an inverse that is a function?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9-12, the graph of a relation is shown. (a) Is the relation a function? (b) Does the relation have an inverse that is a function?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. f(x)=3 x-6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=2 x+5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\frac{2 x-3}{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\frac{x+3}{x-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\sqrt{x-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\sqrt{x+2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=x^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\sqrt{x^{3}+5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\sqrt[3]{x+5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13-22, find a formula for \(f^{-1}(x)\). Give the domain of \(f^{-1}\), including any restrictions inherited from f. \(f(x)=\sqrt[3]{x-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-26, determine whether the function is one-to-one. If it is one-to-one, sketch the graph of the inverse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-26, determine whether the function is one-to-one. If it is one-to-one, sketch the graph of the inverse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-26, determine whether the function is one-to-one. If it is one-to-one, sketch the graph of the inverse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-26, determine whether the function is one-to-one. If it is one-to-one, sketch the graph of the inverse.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=3 x-2 \text { and } g(x)=\frac{x+2}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=\frac{x+3}{4} \text { and } g(x)=4 x-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=x^{3}+1 \text { and } g(x)=\sqrt[3]{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=\frac{7}{x} \text { and } g(x)=\frac{7}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=\frac{x+1}{x} \text { and } g(x)=\frac{1}{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 27-32, confirm that f and g are inverses by showing that and \(f(g(x))=x \text { and } g(f(x))=x\). \(f(x)=\frac{x+3}{x-2} \text { and } g(x)=\frac{2 x+3}{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Currency Conversion In May of 2002 the exchange rate for converting U.S. dollars (x) to euros (y) was y = 108x. (a) How many euros could you get for $100 U.S.? (b) What is the inverse function, and what conversion does it represent? (c) In the spring of 2002, a tourist had an elegant l

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Temperature Conversion The formula for converting Celsius temperature (x) to Kelvin temperature is k(x)=x+273.16. The formula for converting Fahrenheit temperature (x) to Celsius temperature is \(c(x)=(5 / 9)(x-32)\) (a) Find a formula for \(c^{-1}(x)\). What is this formula used for? (b) Fi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which pairs of basic functions (Section 1.3) are inverses of each other?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which basic functions (Section 1.3) are their own inverses?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which basic function can be defined parametrically as follows? \(x=t^{3} \text { and } y=\sqrt{t^{6}} \text { for }-\infty<t<\infty\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which basic function can be defined parametrically as follows? \(x=8 t^{3} \text { and } y=(2 t)^{3} \text { for }-\infty<t<\infty\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
If f is a one-to-one function with domain D and range R, then f-1 is a one-to-one function with domain R and range D. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The set of points (t+1,2 t+3) for all real numbers t form a line with slope 2. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which ordered pair is in the inverse of the relation given by \(x^{2} y+5 y=9 ?\) (A) (2, 1) (B) (-2, 1) (C) (-1, 2) (D) (2, -1) (E) (1, -2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which ordered pair is not in the inverse of the relation given by \(x y^{2}-3 x=12 ?\) (A) (0, -4) (B) (4, 1) (C) (3, 2) (D) (2, 12) (E) (1, -6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which function is the inverse of the function f(x)=3 x-2? (A) \(g(x)=\frac{x}{3}+2\) (B) g(x)=2-3 x (C) \(g(x)=\frac{x+2}{3}\) (D) \(g(x)=\frac{x-3}{2}\) (E) \(g(x)=\frac{x-2}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which function is the inverse of the function \(f(x)=x^{3}+1\)? (A) \(g(x)=\sqrt[3]{x-1}\) (B) \(g(x)=\sqrt[3]{x}-1\) (C) \(g(x)=x^{3}-1\) (D) \(g(x)=\sqrt[3]{x+1}\) (E) \(g(x)=1-x^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Function Properties Inherited by Inverses There are some properties of functions that are automatically shared by inverse functions (when they exist) and some that are not. Suppose that f has an inverse function f-1. Give an algebraic or graphical argument (not a rigorous formal proof) to show that e

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Function Properties Not Inherited by Inverses There are some properties of functions that are not necessarily shared by inverse functions, even if the inverses exist. Suppose that f has an inverse function f-1. For each of the following properties, give an example to show that f can have the property

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Scaling Algebra Grades A teacher gives a challenging algebra test to her class. The lowest score is 52, which she decides to scale to 70. The highest score is 88, which she decides to scale to 97. (a) Using the points (52, 70) and (88, 97), find a linear equation that can be used to convert raw

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn (Continuation of Exercise 47) Explain why it is important for fairness that the scaling function used by the teacher be an increasing function. (Caution: It is not because everyone's grade must go up. What would the scaling function in Exercise 47 do for a student who does enough ext

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Modeling a Fly Ball Parametrically A baseball that leaves the bat at an angle of \((60^{\circ}\) from horizontal traveling 110 feet per second follows a path that can be modeled by the following pair of parametric equations. (You might enjoy verifying this if you have studied motion in physics.)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The Baylor GPA Scale Revisited (See in Section 1.2.) The function used to convert Baylor School percentage grades to GPAs on a 4-point scale is \(y=\left(\frac{3^{1.7}}{30}(x-65)\right)^{\frac{1}{1.7}}+1\) The function has domain [65, 100]. Anything below 65 is a failure and automatically co

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity (Continuation of Exercise 50) The number 1.7 that appears in two places in the GPA scaling formula is called the scaling factor (k). The value of k can be changed to alter the curvature of the graph while keeping the points (65, 1) and (95, 4) fixed. It was felt that the lowest D (65)