Chapter 1

Find the midpoint of the line segment connecting the points. $$ (1.5,2.9),(-5.7,-3.6) $$

Write the number in standard form. \(1 \times 10^{-6}\) (Wavelength in meters of visible light)

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=-2 $$

Find the midpoint of the line segment connecting the points. $$ (9.4,-4.5),(-7.7,9.5) $$

Write the number in standard form. \(9.11 \times 10^{-31}\) (Weight in kilograms of an electron)

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=|x+1| $$

Find the midpoint of the line segment connecting the points. $$ (\sqrt{2}, \sqrt{5}),(\sqrt{2},-\sqrt{5}) $$

Write the number in standard form. \(2 \times 10^{8}\) (Years required for the sun to orbit our galaxy)

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=|2 x-1| $$

Find the midpoint of the line segment connecting the points. $$ (\sqrt{7}, 3 \sqrt{3}),(-\sqrt{7},-\sqrt{3}) $$

Write the number in standard form. \(9 \times 10^{12}\) (Rederal debt in dollars in 2007 )

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=x^{2}-1 $$

Find the midpoint of the line segment connecting the points. $$ (a, b),(-a, 3 b) $$

Write the number in standard form. $$ 1.567 \times 10^{2} $$

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=x^{3} $$

Find the midpoint of the line segment connecting the points. $$ (-a, b),(3 a, b) $$

Write the number in standard form. $$ -5.68 \times 10^{-1} $$

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=2 \sqrt{x} $$

Write the number in standard form. $$ 5 \times 10^{5} $$

Determine if \(f\) is a linear or nonlinear function. If \(f\) is a linear function, determine if \(f\) is a constant function. Support your answer by graphing \(f\). $$ f(x)=\sqrt{x-1} $$

Write the number in standard form. $$ 3.5 \times 10^{3} $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|}\hline\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y & -1 & 3 & 7 & 11 & 15 \end{array} $$

Write the number in standard form. $$ 0.045 \times 10^{5} $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|}\hline\hline x & -4 & -2 & 0 & 2 & 4 \\ \hline y & 1 & -\frac{1}{2} & -2 & -\frac{7}{2} & -5 \end{array} $$

Graph \(y=f(x)\) in the viewing rectangle $$ [-4,7,4,7,1] \text { by }[-3,1,3,1,1] $$ $$ f(x)=3-1.5 x^{2} $$

Write the number in standard form. $$ -5.4 \times 10^{-5} $$

(Refer to Example 3.) Use the given \(f(x)\) to complete the following. (a) Calculate the average rate of change of \(f\) from \(x=1\) to \(x=2\) (b) Illustrate your result from part (a) graphically. $$ f(x)=x^{2} $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|}\hline\hline x & -5 & -3 & 1 & 3 & 5 \\ \hline y & -5 & -2 & 1 & 4 & 7 \end{array} $$

Complete the following. (a) Find the domain and range of the relation. (b) Determine the maximum and minimum of the \(x\) -values and then of the y-values. (c) Label appropriate scales on the xy-axes. (d) Plot the relation. $$ ((0,5),(-3,4),(-2,-5),(7,-3),(0,0)) $$

Write the number in standard form. $$ 67 \times 10^{3} $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|} \hline x & -4 & -2 & 0 & 2 & 4 \\ \hline y & -1 & -1 & -1 & -1 & -1 \\ \hline \end{array} $$

Complete the following. (a) Find the domain and range of the relation. (b) Determine the maximum and minimum of the \(x\) -values and then of the y-values. (c) Label appropriate scales on the xy-axes. (d) Plot the relation. $$ \\{(1,1),(3,0),(-5,-5),(8,-2),(0,3)\\} $$

Write the number in standard form. $$ 0.0032 \times 10^{-1} $$

Compute the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\). Round your answer to two decimal places when appropriate. Interpret your result graphically. $$ f(x)=7 x-2, x_{1}=1, \text { and } x_{2}=4 $$

Use f(x) to determine verbal, graphical and numerical representations. For the numerical representation use a table wish \(x=-2,-1,0,1,2\) Evaluate \(f(2).\) $$ f(x)=x^{2} $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|}\hline\hline x & -4 & 0 & 1 & 2 & 5 \\ \hline y & 5 & 3 & \frac{5}{2} & 2 & \frac{1}{2} \end{array} $$

Complete the following. (a) Find the domain and range of the relation. (b) Determine the maximum and minimum of the \(x\) -values and then of the y-values. (c) Label appropriate scales on the xy-axes. (d) Plot the relation. $$ \\{(2,2),(-3,1),(-4,-1),(-1,3),(0,-2)\\} $$

Evaluate the expression by hand. Write your result in scientific notation and standard form. $$ \left(4 \times 10^{3}\right)\left(2 \times 10^{5}\right) $$

Compute the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\). Round your answer to two decimal places when appropriate. Interpret your result graphically. $$ f(x)=x^{3}-2 x, x_{1}=2, \text { and } x_{2}=4 $$

Decide whether the data are linear or nonlinear. If the data are linear, state the slope \(m\) of the line passing through the data points. $$ \begin{array}{|c|c|c|c|c|c|}\hline\hline x & 10 & 20 & 25 & 35 & 40 \\ \hline y & 40 & 190 & 300 & 600 & 790 \end{array} $$

Use f(x) to determine verbal, graphical and numerical representations. For the numerical representation use a table wish \(x=-2,-1,0,1,2\) Evaluate \(f(2).\) $$ f(x)=2 x-5 $$

Complete the following. (a) Find the domain and range of the relation. (b) Determine the maximum and minimum of the \(x\) -values and then of the y-values. (c) Label appropriate scales on the xy-axes. (d) Plot the relation. $$ \\{(1,1),(2,-3),(-1,-1),(-1,2),(-1,0)\\} $$

Evaluate the expression by hand. Write your result in scientific notation and standard form. $$ \left(3 \times 10^{1}\right)\left(3 \times 10^{4}\right) $$

Compute the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\). Round your answer to two decimal places when appropriate. Interpret your result graphically. $$ f(x)=x^{3}-2 x, x_{1}=2, \text { and } x_{2}=4 $$

Analyzing Real Data For the given data set complete the following. (a) Make a line graph of the data. Let this graph represent a function \(f\) (b) Decide whether \(f\) is linear or nonlinear. Toyota vehicles sold in the United States (millions) $$ \begin{array}{|r|c|c|c|c|}\hline \hline \text { Year } & 1998 & 2000 & 2002 & 2004 \\ \hline \text { Vehicles } & 1.4 & 1.6 & 1.8 & 2.0 \end{array} $$

Use f(x) to determine verbal, graphical and numerical representations. For the numerical representation use a table wish \(x=-2,-1,0,1,2\) Evaluate \(f(2).\) $$ f(x)=|2 x+1| $$

Complete the following. (a) Find the domain and range of the relation. (b) Determine the maximum and minimum of the \(x\) -values and then of the y-values. (c) Label appropriate scales on the xy-axes. (d) Plot the relation. $$ \\{(10,50),(-35,45),(0,-55),(75,25),(-25,-25)\\} $$

Evaluate the expression by hand. Write your result in scientific notation and standard form. $$ \left(5 \times 10^{2}\right)\left(7 \times 10^{-4}\right) $$

Compute the average rate of change of \(f\) from \(x_{1}\) to \(x_{2}\). Round your answer to two decimal places when appropriate. Interpret your result graphically. $$ f(x)=0.5 x^{2}-5, x_{1}=-1, \text { and } x_{2}=4 $$

Analyzing Real Data For the given data set complete the following. (a) Make a line graph of the data. Let this graph represent a function \(f\) (b) Decide whether \(f\) is linear or nonlinear. Interest income after 1 year on an investment earning 7% per year. $$ \begin{array}{|r|r|r|r|r|}\hline \hline \text { Investment } & \$ 500 & \$ 1000 & \$ 2000 & \$ 3500 \\ \hline \text { Interest } & \$ 35 & \$ 70 & \$ 140 & \$ 245 \end{array} $$