Chapter 1

Find the zero of the function \(f\) $$f(x)=1.5 x+2(x-3)+5.5(x+9)$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(\frac{7}{3}\) (The fractional increase in online sales on Thanksgiving Day from 2006 to 2011 )

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

Why is it not possible to write a slope-intercept form of the equation of the line through the points \((12,6)\) and \((12,-2) ?\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Dimensions of a Label The length of a rectangular mail- ing label is 3 centimeters less than twice the width. The perimeter is 54 centimeters. Find its dimensions.

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

Concept Check If \(c\) is a zero of the linear function \(f(x)=m x+b, m \neq 0,\) then the point at which the graph intersects the \(x\) -axis has coordinates \((\longrightarrow, \longrightarrow)\)

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(-3.5\) (The amount in billions of dollars that the Motion Picture Association of America estimates is lost annually due to piracy)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Dimensions of a Square If the length of a side of a square is increased by 3 centimeters, the perimeter of the new square is 40 centimeters more than twice the length of the side of the original square. Find the length of the side of the original square.

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 \(f\) $$f(x)=2-\frac{1}{2} x$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(5 \sqrt{2}\) (The length of the diagonal of a square measuring 5 units on each side)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ World's Largest Easel The painting on the world's largest easel has a perimeter of 112 feet. Its length is 96 inches more than its width. What is its length in feet? (Source: Roadside America.)

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 \(f\) $$f(x)=\frac{1}{4} x+\frac{1}{2}$$

Classify each number as one or more of the following: natural number, integer, rational number, or real number. \(\pi\) (The ratio of the circumference of a circle to its diameter)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ The aspect ratio of older television monitors is \(4: 3 .\) One such television has a rectangular viewing screen with perimeter 98 inches. What are the length and width of the screen? since televisions are advertised by the diagonal measure of their screens, how would this monitor be advertised? (IMAGE CAN'T COPY)

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 \(f\) $$f(x)=\frac{1}{3} x$$

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Populations of cities

bWork 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 \(f\) $$f(x)=-3 x$$

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Distances to nearby cities on road signs

Explain how to determine whether a parenthesis or a square bracket is used when graphing an inequality on a number line.

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((4,8)\) and \((0,4)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Dimensions of a Puzzle Piece\(\quad\) A puzzle piece in the shape of a triangle has perimeter 30 centimeters. Two sides of the triangle are each twice as long as the shortest side. Find the length of the shortest side.

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 \(f\) $$f(x)=0.4 x+0.15$$

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Shoe sizes

Concept Check \(\quad\) The three-part inequality \(a

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((3,6)\) and \((0,10)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Perimeter of a Plot of Land The perimeter of a triangular plot of land is 2400 feet. The longest side is 200 feet less than twice the shortest. The middle side is 200 feet less than the longest side. Find the lengths of the three sides of the triangular plot.

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 \(f\) $$f(x)=x+0.5$$

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Prices paid (in dollars and cents) for gasoline tank fill-ups

Sketch the graph of \(f\) by hand. $$f(x)=x-3$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((3,-8)\) and \((5,-3)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Motion\(\quad\) A car went 372 miles in 6 hours, traveling part of the time at 55 miles per hour and part of the time at 70 miles per hour. How long did the car travel at each speed?

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 \(f\) $$f(x)=\frac{2-x}{4}$$

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Daily low winter temperatures in U.S. cities

Sketch the graph of \(f\) by hand. $$f(x)=1-2 x$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((-5,4)\) and \((-3,2)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Running At 2: 00 P.M. a runner heads north on a highway, jogging at 10 miles per hour. At 2: 30 P.M. a driver heads north on the same highway to pick up the runner. If the car travels at 55 miles per hour, how long will it take the driver to catch the runner?

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 \(f\) $$f(x)=\frac{3-3 x}{6}$$

If you were asked to solve \(2 x+3=4 x-12\) by the \(x\) -intercept method, why would you not get the correct answer by graphing \(y_{1}=2 x+3-4 x-12 ?\)

For each measured quantity, state the set of numbers that is most appropriate to describe it. Choose from the natural numbers, integers, and rational numbers. Golf scores relative to par

Sketch the graph of \(f\) by hand. $$f(x)=3$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((2,3.5)\) and \((6,-2.5)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Acid Mixture How many gallons of a \(5 \%\) acid solution must be mixed with 5 gallons of a \(10 \%\) solution to obtain a \(7 \%\) solution?

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 \(f\) $$f(x)=\frac{x+5}{15}$$

Graph each set of numbers on a number line. $$\\{-4,-3,-2,-1,0,1\\}$$

Sketch the graph of \(f\) by hand. $$f(x)=-4$$

Find the slope-intercept form of the equation of the line satisfying the given conditions. Do not use a calculator. Through \((-1,6.25)\) and \((2,-4.25)\)

$$\begin{aligned} &\text {Solve each problem analytically, and support your solution}\\\ &\text {graphically.} \end{aligned}$$ Acid Mixture Bill Charlson needs \(10 \%\) hydrochloric acid for a chemistry experiment. How much \(5 \%\) acid should he mix with 60 milliliters of \(20 \%\) acid to obtain a \(10 \%\) solution?

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 \(f\) $$f(x)=\frac{x-4}{2}$$

Concept Check If the \(x\) -intercept method leads to a horizontal line that coincides with the \(x\) -axis, what is the solution set of the equation? What special name is given to this kind of equation?