Chapter 4

In \(7-10,\) the domain of each function is the set of real numbers. a. Sketch the graph of each function. b. What is the range of each function? $$ y=|x-1| $$

In \(3-8,\) for each function: a. Write an expression for \(f(x) .\) b. Find \(f(5)\) \(y=\sqrt{x-1}\)

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \((g+f)(x)\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. Each day, Jaymee works for 6 hours typing \(p\) pages of a report at a rate of \(m\) minutes per page.

In \(3-10\) , the coordinates of point \(P\) on the circle with center at \(C\) are given. Write an equation of each circle: a. in center-radius form b. in standard form. $$ P(0,-3), C(6,5) $$

In \(3-10,\) find each of the function values when \(\mathrm{f}(x)=4 x\) $$ \mathrm{f}\left(\mathrm{f}^{-1}(-6)\right) $$

In \(3-10\) , evaluate each composition for the given values if \(f(x)=3 x\) and \(g(x)=x-2\) $$ \mathrm{g}(\mathrm{g}(5)) $$

In \(7-10,\) the domain of each function is the set of real numbers. a. Sketch the graph of each function. b. What is the range of each function? $$ y=|3 x+9| $$

In \(3-8,\) for each function: a. Write an expression for \(f(x) .\) b. Find \(f(5)\) \(x \stackrel{\mathrm{f}}{\rightarrow} \frac{2}{x}\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. Each day, Sophia works for \(h\) hours typing \(p\) pages of a report at a rate of 15 minutes per page.

In \(3-10\) , the coordinates of point \(P\) on the circle with center at \(C\) are given. Write an equation of each circle: a. in center-radius form b. in standard form. $$ P(1,1), C(6,13) $$

In \(3-10,\) find each of the function values when \(\mathrm{f}(x)=4 x\) $$ \mathrm{f}^{-1}(\mathrm{f}(-6)) $$

In \(3-10\) , evaluate each composition for the given values if \(f(x)=3 x\) and \(g(x)=x-2\) $$ \mathrm{f}\left(\mathrm{g}\left(\frac{2}{3}\right)\right) $$

In \(7-10,\) the domain of each function is the set of real numbers. a. Sketch the graph of each function. b. What is the range of each function? $$ \mathrm{f}(x)=|4 x|+1 $$

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(f(x)=7-x\)

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \((\mathrm{gh})(x)\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. Each day, Brandon works for \(h\) hours typing 40 pages of a report at a rate of \(m\) minutes per page.

In \(3-10\) , the coordinates of point \(P\) on the circle with center at \(C\) are given. Write an equation of each circle: a. in center-radius form b. in standard form. $$ P(4,2), C(0,1) $$

In \(3-10,\) find each of the function values when \(\mathrm{f}(x)=4 x\) $$ \mathrm{f}\left(\mathrm{f}^{-1}(\sqrt{2})\right) $$

In \(3-10\) , evaluate each composition for the given values if \(f(x)=3 x\) and \(g(x)=x-2\) $$ g\left(f\left(\frac{2}{3}\right)\right) $$

In \(7-10,\) the domain of each function is the set of real numbers. a. Sketch the graph of each function. b. What is the range of each function? $$ g(x)=\left|3-\frac{x}{2}\right|-3 $$

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(0,8),(1,7),(2,6),(3,5),(4,4)\\} $$

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \(\left(\frac{g}{f}\right)(x)\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. Each day, I am awake \(a\) hours and I sleep \(s\) hours.

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ \mathrm{f}(x)=2 x+1, \mathrm{g}(x)=4 x $$

\(A(2,7)\) is a fixed point in the coordinate plane. Let \(B(x, 7)\) be any point on the same horizontal line. If \(A B=\mathrm{h}(x),\) express \(\mathrm{h}(x)\) in terms of \(x .\)

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(y=1+x^{2}\)

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(1,4),(2,7),(1,10),(4,13)\\} $$

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \((g+3 f)(x)\)

In \(6-12,\) tell whether the variables vary directly, inversely, or neither. A bank pays 4\(\%\) interest on all savings accounts. A depositor receives \(I\) dollars in interest when the balance in the savings account is \(P\) dollars.

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ f(x)=3 x, g(x)=x-1 $$

In \(12-17,\) use a graph to find the solution set of each inequality. $$ x^{2}+2 x-3 < 0 $$

Along the New York State Thruway there are distance markers that give the number of miles from the beginning of the thruway. Brianna enters the thruway at distance marker \(150 .\) a. If \(\mathrm{m}(x)=\) the number of miles that Brianna has traveled on the thruway, write an equation for \(\mathrm{m}(x)\) when she is at distance marker \(x\) . b. Write an equation for \(\mathrm{h}(x),\) the number of hours Brianna required to travel to distance marker \(x\) at 65 miles per hour

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(f(x)=4\)

In \(8-13\) , the domain of \(f(x)=4-2 x\) and of \(g(x)=x^{2}\) is the set of real numbers and the domain of \(h(x)=\frac{1}{x}\) is the set of non-zero real numbers. a. Write each function value in terms of \(x\) . b. Find the domain of each function. \((-g f)(x)\)

Rectangles \(A B C D\) and \(E F G H\) have the same area. The length of \(A B C D\) is equal to twice the length of the \(E F G H\) . How does the width of \(A B C D\) compare to the width of \(E F G H ?\)

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ \mathrm{f}(x)=x^{2}, \mathrm{g}(x)=4+x $$

In \(13-20\) : a. Graph each function. b. Is the function a direct variation? \(c\) . Is the function one-to-one? \(y=3 x\)

a. Sketch the graph of \(y=|x|\) b. Sketch the graph of \(y=|x|+2\) c. Sketch the graph of \(y=|x|-2\) d. Describe the graph of \(y=|x|+a\) in terms of the graph of \(y=|x|\)

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(y=\sqrt{1-x}\)

In \(12-23,\) each set is a function from set \(A\) to set \(B .\) a. What is the largest subset of the real numbers that can be set \(A\) , the domain of the given function? b. If set \(A=\operatorname{set} B,\) is the function onto? Justify your answer. $$ \\{(x, y) : y=5-x\\} $$

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(2,7),(3,7),(4,7),(5,7),(6,7)\\} $$

When Brian does odd jobs, he charges ten dollars an hour plus two dollars for transportation. When he works for Mr. Atkins, he receives a 15\(\%\) tip based on his wages for the number of hours that he works but not on the cost of transportation. a. Find \(c(x),\) the amount Brian charges for \(x\) hours of work. b. Find \(t(x),\) Brian's tip when he works for \(x\) hours. c. Find \(c(x),\) Brian's earnings when he works for Mr. Atkins for \(x\) hours, if \(c(x)=c(x)+t(x)\) d. Find e( 3 ), Brian's earnings when he works for Mr. Atkins for 3 hours.

Aaron can ride his bicycle to school at an average rate that is three times that of the rate at which he can walk to school. How does the time that it takes Aaron to ride to school compare with the time that it takes him to walk to school?

In \(11-18 :\) a. Find \(h(x)\) when \(h(x)=g(f(x)) .\) b. What is the domain of \(h(x) ?\) c. What is the range of \(\mathrm{h}(x) ?\) d. Graph \(\mathrm{h}(x)\) $$ f(x)=4+x, g(x)=x^{2} $$

In \(13-20\) : a. Graph each function. b. Is the function a direct variation? \(c\) . Is the function one-to-one? \(y=6-x\)

a. Sketch the graph of \(y=|x| .\) b. Sketch the graph of \(y=|x+2|\) c. Sketch the graph of \(y=|x-2|\) d. Describe the graph of \(y=|x+a|\) in terms of the graph of \(y=|x|\)

\(\operatorname{In} 9-14, y=f(x) .\) Find \(f(-3)\) for each function. \(\mathrm{f}(x)=|x+2|\)

In \(11-16,\) determine if the function has an inverse. If so, list the pairs of the inverse function. If not, explain why there is no inverse function. $$ \\{(-1,3),(-1,5),(-2,7),(-3,9),(-4,11)\\} $$

Mrs. Cucci makes candy that she sells for \(\$ 8.50\) a pound. When she ships the candy to out- of town customers, she adds a flat shipping charge of \(\$ 2.00\) plus an additional \(\$ 0.50\) per pound. a. Find \(c(x),\) the cost of \(x\) pounds of candy. b. Find \(s(x),\) the cost of shipping \(x\) pounds of candy. c. Find \(t(x),\) the total bill for \(x\) pounds of candy that has been shipped, if \(t(x)=c(x)+s(x)\) d. Find \(t(5),\) the total bill for five pounds of candy that is shipped.