Chapter 1

Evaluate by hand. $$ \frac{4+9}{2+3}-\frac{-3^{2} \cdot 3}{5} $$

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=6-3 x \text { for } x=-1, a+1 $$

Find the exact distance between the two points. Where appropriate, also give approximate results to the nearest hundredth. $$ (40,6),(-20,17) $$

State the slope of the graph of \(f\). Interpret this slope. $$ f(x)=\frac{2}{3} x $$

Evaluate by hand. $$ 10 \div 2 \div \frac{5+10}{5} $$

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=\frac{3 x-5}{x+5} \text { for } x=-1, a $$

Find the exact distance between the two points. Where appropriate, also give approximate results to the nearest hundredth. $$ (a, 0),(0,-b) $$

State the slope of the graph of \(f\). Interpret this slope. $$ f(x)=-5 $$

Evaluate by hand. $$ -5^{2}-20 \div 4-2 $$

State the slope of the graph of \(f\). Interpret this slope. $$ f(x)=x+5 $$

Evaluate by hand. $$ 5-(-4)^{3}-(4)^{3} $$

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=x^{2}-x+1 \text { for } x=1,-2 $$

An isosceles triangle has at least two sides of equal length. Determine whether the triangle with vertices \((0,0),(3,4),(7,1)\) is isosceles.

State the slope of the graph of \(f\). Interpret this slope. $$ f(x)=9-x $$

Write the number in scientific notation. \(184,800\) (New lung cancer cases reported in 2005 )

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=\frac{1}{x^{2}} \text { for } x=4,-7 $$

An equilateral triangle has sides of equal length. Determine whether the triangle with vertices \((-1,-1),(2,3),(-4,3)\) is equilateral.

State the slope of the graph of \(f\). Interpret this slope. $$ f(x)=23 $$

Write the number in scientific notation. \(29,285,000\) (People worldwide living with HTV)

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=\sqrt{x-3} \text { for } x=4, a+4 $$

At 9: 00 A.M. car \(A\) is traveling north at 50 miles per hour and is located 50 miles south of car \(\mathbf{B}\). Car \(\mathbf{B}\) is traveling west at 20 miles per hour. (a) Let \((0,0)\) be the initial coordinates of car \(\mathbf{B}\) in the \(x y\) -plane, where units are in miles. Plot the locations of each car at 9: 00 A.M. and at 11: 00 A.M. (b) Find the distance \(d\) between the cars at 11: 00 A.M.

Write the number in scientific notation. 0.04361 (Proportion of U.S. deaths attributed to accidents in 2004 )

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=\frac{1}{x^{2}-9} \text { for } x=4, a-5 $$

Two ships leave a harbor at the same time. The first ship heads north at 20 miles per hour, and the second ship heads west at 15 miles per hour. Write an expression that gives the distance \(d\) between the ships after \(t\) hours.

Write the number in scientific notation. 0.62 (Number of miles in 1 kilometer)

Use the midpoint formula for the following. The average life expectancy for a female born in the United States was 77.4 years in 1980 and 79.5 years in 2000 . Estimate the average life expectancy for a female born in 1990 . (Actual life expectancy was \(78.8 .\) ) (Source: Bureau of the Census.)

The function given by \(P(x)=19.4 x\) calculates the pounds of \(\mathrm{CO}_{2}\) (carbon dioxide) released into the atmosphere by a car burning \(x\) gallons of gasoline. (a) Calculate \(P(20)\) and interpret the result. (b) Find the slope of the graph of \(P\). Interpret this slope as a rate of change.

Write the number in scientific notation. $$ 2450 $$

Use the midpoint formula for the following. In 1990 there were \(773,919\) inmates in state and federal prisons, and in 2000 there were \(1,391,892 .\) Estimate the number of inmates in 1995\. (Actual number was \(1,125,874\).) (Source: Department of Justice.)

The distance \(D\) in miles that a train is from a station after \(x\) hours is given by the formula \(D(x)=150-20 x\) (a) Calculate \(D(5)\) and interpret the result. (b) Find the slope of the graph of \(D .\) Interpret this slope as a rate of change.

Write the number in scientific notation. $$ 105.6 $$

Complete the following. (a) Find \(f(x)\) for the indicated values of \(x\), if possible. (b) Find the domain of \(f\). $$ f(x)=\frac{1}{\sqrt{x-1}} \text { for } x=0, a^{2}-a+1 $$

In the Olympic Games, the 200 -meter dash is run in approximately 20 seconds. Estimate the time to run the 100 -meter dash.

A driver's distance \(D\) in miles from a rest stop after \(x\) hours is given by \(D(x)=75 x\) (a) How far is the driver from the rest stop after 2 hours? (b) Find the slope of the graph of \(D .\) Interpret this slope as a rate of change.

Write the number in scientific notation. $$ 0.56 $$

The median age of the U.S. population for each year \(t\) between 1970 and 2010 can be approximated by the formula \(A(t)=0.243 t-450.8\). (a) Compute the median ages in 1980 and 2000 . (b) What is the slope of the graph of \(A ?\) Interpret the slope.

Between any two real numbers \(a\) and \(b\) there is always another real number. How could such a number be found?

Write the number in scientific notation. $$ -0.00456 $$

A car's distance from a service center along a straight highway can be described by a constant function of time. What can be said about the car's velocity?

Find the midpoint of the line segment connecting the points. $$ (1,2),(5,-3) $$

Write the number in scientific notation. $$ -0.0087 $$

Find the midpoint of the line segment connecting the points. $$ (-6,7),(9,-4) $$

Write the number in scientific notation. $$ 1,250,000 $$

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 \(f\). $$ f(x)=-2 x+5 $$

Find the midpoint of the line segment connecting the points. $$ (-30,50),(50,-30) $$

Write the number in scientific notation. $$ 206.8 $$

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 \(f\). $$ f(x)=3 x-2 $$

Find the midpoint of the line segment connecting the points. $$ (28,-33),(52,38) $$

Write the number in scientific notation. $$ 0.00007 $$

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 \(f\). $$ f(x)=1 $$