Chapter 1

Using interval notation, write each set. Then graph it on a number line. $$\\{x |-1

$$\text { Work Exercises } 1-6 \text { mentally. Do not use a calculator.}$$ If \(40 \mathrm{L}\) of an acid solution is \(75 \%\) acid, how much pure acid is there in the mixture?

Find the zero of the function \(f\) $$f(x)=-3 x-12$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((1,3), m=-2\)

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=x-4$$

For each set, list all elements that belong to the (a) natural numbers (b) whole numbers (c) integers (d) rational numbers (e) irrational numbers (f) real numbers $$\left\\{-6,-\frac{12}{4},-\frac{5}{8},-\sqrt{3}, 0,0.31,0 . \overline{3}, 2 \pi, 10, \sqrt{17}\right\\}$$

Using interval notation, write each set. Then graph it on a number line. $$\\{x | x \geq-3\\}$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((2,4), m=-1\)

$$\text { Work Exercises } 1-6 \text { mentally. Do not use a calculator.}$$ If \(y\) varies directly with \(x,\) and \(y=2\) when \(x=4,\) what is the value of \(y\) when \(x=12 ?\)

Find the zero of the function \(f\) $$f(x)=5 x-30$$

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=-x+4 \quad$$

For each set, list all elements that belong to the (a) natural numbers (b) whole numbers (c) integers (d) rational numbers (e) irrational numbers (f) real numbers $$\left\\{-8,-\frac{14}{7},-0.245,0, \frac{6}{2}, 8, \sqrt{81}, \sqrt{12}\right\\}$$

Using interval notation, write each set. Then graph it on a number line. $$\\{x | x<0\\}$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((-5,4), m=1.5\)

Find the zero of the function \(f\) $$f(x)=5 x$$

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=3 x-6 \quad$$

Using interval notation, write each set. Then graph it on a number line. $$\\{x | 8>x>3\\}$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((-4,3), m=0.75\)

$$\text { Work Exercises } 1-6 \text { mentally. Do not use a calculator.}$$ Suppose that a computer that originally sold for \(x\) dollars has been discounted \(30 \% .\) Which one of the following expressions does not represent the sale price of the computer? A. \(x-0.30 x\) B. \(0.70 x \quad\) C. \(\frac{7}{10} x\) D. \(x-0.30\)

Find the zero of the function \(f\) $$f(x)=-2 x$$

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=\frac{2}{3} x-2$$

For each set, list all elements that belong to the (a) natural numbers (b) whole numbers (c) integers (d) rational numbers (e) irrational numbers (f) real numbers $$\\{-\sqrt{49},-0.405,-0 . \overline{3}, 0.1,3,18,6 \pi, 56\\}$$

Using interval notation, write each set. Then graph it on a number line. $$\\{x | 1 \leq x<2\\}$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((-8,1), m=-0.5\)

$$\text { Work Exercises } 1-6 \text { mentally. Do not use a calculator.}$$ Consider the following problem. One number is three less than six times a second number. Their sum is \(32 .\) Find the numbers. If \(x\) represents the second number, which equation is correct for solving this problem? A. \(32-(x+3)=6 x\) B. \((3-6 x)+x=32\) C. \(32-(3-6 x)=x\) D. \((6 x-3)+x=32\)

Find the zero of the function \(f\) $$f(x)=2(3 x-5)+8(4 x+7)$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(16,351,000,000,000\) (The federal debt in dollars in January 2013 )

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=-\frac{2}{5} x+2$$

Using interval notation, write each set. Then graph it on a number line. $$\\{x |-5

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \((-5,9), m=-0.75\)

$$\text { Work Exercises } 1-6 \text { mentally. Do not use a calculator.}$$ Consider the following problem: The difference between six times a number and 9 is equal to five times the sum of the number and 2. Find the number. If \(x\) represents the number, which equation is correct for solving this problem? A. \(6 x-9=5(x+2)\) B. \(9-6 x=5(x+2)\) C. \(6 x-9=5 x+2\) D. \(9-6 x=5 x+2\)

Find the zero of the function \(f\) $$f(x)=-4(2 x-3)+8(2 x+1)$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(700,000,000,000\) (The federal 2008 bailout fund in dollars)

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=\frac{4}{3} x-3$$

Using the variable \(x\), write each interval using set-builder notation. $$(-4,3)$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \(\left(\frac{1}{2},-4\right), m=2\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ The perimeter of a rectangle is 98 centimeters. The width is 19 centimeters. Find the length.

Find the zero of the function \(f\) $$f(x)=3 x+6(x-4)$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(-25\) (The percent change in the number of Yahoo searches from 2011 to 2012 )

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=3 x$$

Using the variable \(x\), write each interval using set-builder notation. $$[2,7)$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \(\left(5,-\frac{1}{3}\right), m=3\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Perimeter of a Storage Shed A carpenter must build a rectangular storage shed. She wants the length to be 3 feet greater than the width, and the perimeter must be 22 feet. Find the length and the width of the shed.

Find the zero of the function \(f\) $$f(x)=-8 x+0.5(2 x+8)$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(-3\) (The annual percent change in the area of tropical rain forests)

Give the (a) \(x\) -intercept, (b) \(y\) -intercept, (c) domain, (d) range, and (e) slope of the line. Do not use a calculator. $$f(x)=-0.5 x$$

Using the variable \(x\), write each interval using set-builder notation. $$(-\infty,-1]$$

Write the slope-intercept form of the line that passes through the given point with slope \(m .\) Do not use a calculator. Through \(\left(\frac{1}{4}, \frac{2}{3}\right), m=\frac{1}{2}\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Dimensions of a Label The length of a rectangular label is 2.5 centimeters less than twice the width. The perimeter is 40.6 centimeters. Find the width.

Work each problem related to linear functions. (a) Evaluate \(f(-2)\) and \(f(4)\) (b) Graph \(f\). How can the graph of \(f\) be used to determine the zero of \(f ?\) (c) Find the zero of \(f\) $$f(x)=x+2$$