Question 1

For each of the functions, determine the
(i) domain
(ii) range
(iii) $x$-intercept(s)
(iv) $y$-intercept(s).
(a)
  
(b)
  
(c)

Accepted Answer

(a) (i) $(-\infty, \infty)$
(ii) $(-\infty, 4]$
(iii) -3 and 1
(iv) 2
(b) (i) $(-\infty, \infty)$
(ii) $[-1, \infty)$
(iii) -4 and -1
(iv) 2
(c) (i) $(-\infty, \infty)$
(ii) $(-\infty, \infty)$
(iii) 2
(iv) -1.5

Question 2

Use the figure to solve each equation or inequality.
(a) $f(x)=g(x)$
(b) $f(x)<g(x)$
(c) $f(x) \geq g(x)$
(d) $y_{2}-y_{1}=0$

Accepted Answer

(a) $x=2$
(b) $(-\infty, 2)$
(c) $[2, \infty)$
(d) $x=2$

Question 3

Use the screen to solve the equation or inequality. Here the function $y_{1}=f(x)$ is a linear function defined over the domain of real numbers.
(a) $y_{1}=0$
(b) $y_{1} \leq 0$
(c) $y_{1} \geq 0$
(d) $y_{1}>0$

Accepted Answer

(a) $x=-4$
(b) $[-4, \infty)$
(c) $(-\infty,-4]$
(d) $(-\infty,-4)$

Question 4

Consider the linear functions $f(x)=\frac{3}{4}(4-x)+x-8$ and $g(x)=3(x-3)+2(x+2)$.
(a) Solve $f(x)=g(x)$ analytically, showing all steps. Also, check analytically.
(b) Graph $y_{1}=f(x)$ and $y_{2}=g(x)$ and use your result in part (a) to find the solution set of $f(x)<g(x)$. Explain your answer.
(c) Repeat part (b) for $f(x)>g(x)$

Accepted Answer

The answer of Consider the linear functions $f(x)=\frac{3}{4}(4-x)+x-8$ and $g(x)=3(x-3)+2(x+2)$.
(a)...

Question 5

Consider the linear function $f(x)=\frac{1}{4}(5 x-8)-(x-3)$.
(a) Solve the equation $f(x)=0$ analytically.
(b) Solve the inequality $f(x) \leq 0$ analytically.
(c) Graph $y=f(x)$ in an appropriate viewing window and explain how the graph supports your answers in parts (a) and (b).

Accepted Answer

The answer of Consider the linear function $f(x)=\frac{1}{4}(5 x-8)-(x-3)$.
(a) Solve...

Question 6

During the period from 1996 to 2006 the average annual cost (in dollars) of tuition and fees at private four-year colleges rose in an approximately linear fashion. The graph depicts this growth using a line segment. (Source: The College Board)
  
(a) Use the midpoint formula to approximate the cost during the year 2001.
(b) Find the slope of the line and explain its meaning in the context of this situation.

Accepted Answer

The answer of During the period from 1996 to 2006...

Question 7

Find the equation of the line passing through the point $(1,-4)$ and
(a) parallel to the line with equation $y=2 x+3$.
(b) perpendicular to the line with equation $3 x+y=0$.

Accepted Answer

The answer of Find the equation of the line passing...

Question 8

Find the $x$ - and $y$-intercepts of the line whose standard form is $-3 x+2 y=9$. What is the slope of this line?

Accepted Answer

The answer of Find the $x$ - and $y$-intercepts of...

Question 9

Give the equations of both the horizontal and vertical lines passing through the point $(-2,12)$.

Accepted Answer

The answer of Give the equations of both the horizontal...

Question 10

The table lists the Gross Domestic Product (GDP) from 2004 to 2008 in billions of dollars. (Source: U.S. Department of Commerce)
  
(a) Find the least-squares regression line for the data. Give the correlation coefficient.
(b) Use this line to predict the federal debt in 2009.

Accepted Answer

The answer of The table lists the Gross Domestic Product...

Question 11

Suppose that an empty circular wading pool has a radius of 7 feet. During a storm, rain falling at a rate of 1 inch per hour begins to fill the pool. A small drain at the bottom of the pool is capable of draining 35 gallons of water per hour.
(a) Determine the number of cubic inches of water falling into the pool in one hour. (Hint: Each hour a layer of water 1 inch thick falls into the pool.)
(b) One gallon of water equals about 231 cubic inches. Write a formula for a function $g$ that computes the gallons of water landing in the pool in $x$ hours.
(c) How many gallons of water land in the pool during a 3 hour storm?
(d) Will the drain be able to keep up with the rainfall? If not, how many such drains would be needed?

Accepted Answer

The answer of Suppose that an empty circular wading pool...

Question 12

For each of the functions, determine the 
(i) domain 
(ii) range 
(iii) x-intercept(s) 
(iv) y-intercept(s).
(a)  
(b)  
(c)

Accepted Answer

The answer of For each of the functions, determine the...

Question 13

Use the figure to solve each equation or inequality.
(a) $f(x)=g(x)$
(b) $f(x)<g(x)$
(c) $f(x) \geq g(x)$
(d) $y_{2}-y_{1}=0$

Accepted Answer

The answer of Use the figure to solve each equation...

Question 14

Use the screen to solve the equation or inequality. Here the function $y_{1}=f(x)$ is a linear function defined over the domain of real numbers.
(a) $y_{1}=0$ 
(b) $y_{1}<0$
(c) $y_{1}>0$
(d) $y_{1} \leq 0$

Accepted Answer

The answer of Use the screen to solve the equation...

Question 15

Consider the linear functions $f(x)=4-3 x+4(x+1)$ and $g(x)=3(x+1)-5(x+2)$.
(a) Solve $f(x)=g(x)$ analytically, showing all steps. Also, check analytically.
(b) Graph $y_{1}=f(x)$ and $y_{2}=g(x)$ and use your result in part (a) to find the solution set of $f(x)<g(x)$. Explain your answer.
(c) Repeat part (b) for $f(x)>g(x)$.

Accepted Answer

The answer of Consider the linear functions $f(x)=4-3 x+4(x+1)$ and...

Question 16

Consider the linear function $f(x)=3(x-1)-\frac{1}{3}(6 x-9)$.
(a) Solve the equation $f(x)=0$ analytically.
(b) Solve the inequality $f(x) \leq 0$ analytically.
(c) Graph $y=f(x)$ in an appropriate viewing window and explain how the graph supports your answers in parts (a) and (b).

Accepted Answer

The answer of Consider the linear function $f(x)=3(x-1)-\frac{1}{3}(6 x-9)$.
(a) Solve...

Question 17

For the years 1996 to 2000, it was estimated that Medicare costs (in billions of dollars) would rise in a linear fashion. See the graph below. (Source: U.S. Office of Management and Budget)
  
(a) Use the midpoint formula to approximate Medicare costs during the year 1998.
(b) Find the slope of the line and explain its meaning in the context of this situation.

Accepted Answer

The answer of For the years 1996 to 2000, it...

Question 18

Find the equation of the line passing through the point $(2,-1)$ and
(a) parallel to the line with equation $y=\frac{1}{2} x+3$.
(b) perpendicular to the line with equation $-3 x-y=4$.

Accepted Answer

The answer of Find the equation of the line passing...

Question 19

Find the $x$ - and $y$-intercepts of the line whose standard form is $3 x+7 y=-9$.
What is the slope of this line?

Accepted Answer

The answer of Find the $x$ - and $y$-intercepts of...

Question 20

Give the equations of both the horizontal and vertical lines passing through the point $(7,3)$.

Accepted Answer

The answer of Give the equations of both the horizontal...

Quiz 1: Linear Functions, Equations, and Inequalities

For each of the functions, determine the (i) domain (ii) range (iii) $x$ -intercept(s) (iv) $y$ -intercept(s). (a) (b) (c)

Use the figure to solve each equation or inequality. (a) $f(x)=g(x)$ (b) $f(x)<g(x)$ (c) $f(x) \geq g(x)$ (d) $y_{2}-y_{1}=0$ $Use the figure to solve each equation or inequality. (a) f(x)=g(x) (b) f(x)<g(x) (c) f(x) \geq g(x) (d) y_{2}-y_{1}=0$

Consider the linear function $f(x)=\frac{1}{4}(5 x-8)-(x-3)$ . (a) Solve the equation $f(x)=0$ analytically. (b) Solve the inequality $f(x) \leq 0$ analytically. (c) Graph $y=f(x)$ in an appropriate viewing window and explain how the graph supports your answers in parts (a) and (b).

Find the equation of the line passing through the point $(1,-4)$ and (a) parallel to the line with equation $y=2 x+3$ . (b) perpendicular to the line with equation $3 x+y=0$ .

Find the $x$ - and $y$ -intercepts of the line whose standard form is $-3 x+2 y=9$ . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point $(-2,12)$ .

The table lists the Gross Domestic Product (GDP) from 2004 to 2008 in billions of dollars. (Source: U.S. Department of Commerce) (a) Find the least-squares regression line for the data. Give the correlation coefficient. (b) Use this line to predict the federal debt in 2009.

For each of the functions, determine the (i) domain (ii) range (iii) x-intercept(s) (iv) y-intercept(s). (a) (b) (c)

Use the figure to solve each equation or inequality. (a) $f(x)=g(x)$ (b) $f(x)<g(x)$ (c) $f(x) \geq g(x)$ (d) $y_{2}-y_{1}=0$ $Use the figure to solve each equation or inequality. (a) f(x)=g(x) (b) f(x)<g(x) (c) f(x) \geq g(x) (d) y_{2}-y_{1}=0$

Consider the linear function $f(x)=3(x-1)-\frac{1}{3}(6 x-9)$ . (a) Solve the equation $f(x)=0$ analytically. (b) Solve the inequality $f(x) \leq 0$ analytically. (c) Graph $y=f(x)$ in an appropriate viewing window and explain how the graph supports your answers in parts (a) and (b).

Find the equation of the line passing through the point $(2,-1)$ and (a) parallel to the line with equation $y=\frac{1}{2} x+3$ . (b) perpendicular to the line with equation $-3 x-y=4$ .

Find the $x$ - and $y$ -intercepts of the line whose standard form is $3 x+7 y=-9$ . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point $(7,3)$ .

Quiz 1: Linear Functions, Equations, and Inequalities

For each of the functions, determine the (i) domain (ii) range (iii) xxx -intercept(s) (iv) yyy -intercept(s). (a) (b) (c)

Use the figure to solve each equation or inequality. (a) f(x)=g(x)f(x)=g(x)f(x)=g(x) (b) f(x)<g(x)f(x)<g(x)f(x)<g(x) (c) f(x)≥g(x)f(x) \geq g(x)f(x)≥g(x) (d) y2−y1=0y_{2}-y_{1}=0y2​−y1​=0

Use the screen to solve the equation or inequality. Here the function y1=f(x)y_{1}=f(x)y1​=f(x) is a linear function defined over the domain of real numbers. (a) y1=0y_{1}=0y1​=0 (b) y1≤0y_{1} \leq 0y1​≤0 (c) y1≥0y_{1} \geq 0y1​≥0 (d) y1>0y_{1}>0y1​>0

Find the equation of the line passing through the point (1,−4)(1,-4)(1,−4) and (a) parallel to the line with equation y=2x+3y=2 x+3y=2x+3 . (b) perpendicular to the line with equation 3x+y=03 x+y=03x+y=0 .

Find the xxx - and yyy -intercepts of the line whose standard form is −3x+2y=9-3 x+2 y=9−3x+2y=9 . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point (−2,12)(-2,12)(−2,12) .

The table lists the Gross Domestic Product (GDP) from 2004 to 2008 in billions of dollars. (Source: U.S. Department of Commerce) (a) Find the least-squares regression line for the data. Give the correlation coefficient. (b) Use this line to predict the federal debt in 2009.

For each of the functions, determine the (i) domain (ii) range (iii) x-intercept(s) (iv) y-intercept(s). (a) (b) (c)

Use the figure to solve each equation or inequality. (a) f(x)=g(x)f(x)=g(x)f(x)=g(x) (b) f(x)<g(x)f(x)<g(x)f(x)<g(x) (c) f(x)≥g(x)f(x) \geq g(x)f(x)≥g(x) (d) y2−y1=0y_{2}-y_{1}=0y2​−y1​=0

Use the screen to solve the equation or inequality. Here the function y1=f(x)y_{1}=f(x)y1​=f(x) is a linear function defined over the domain of real numbers. (a) y1=0y_{1}=0y1​=0 (b) y1<0y_{1}<0y1​<0 (c) y1>0y_{1}>0y1​>0 (d) y1≤0y_{1} \leq 0y1​≤0

Find the equation of the line passing through the point (2,−1)(2,-1)(2,−1) and (a) parallel to the line with equation y=12x+3y=\frac{1}{2} x+3y=21​x+3 . (b) perpendicular to the line with equation −3x−y=4-3 x-y=4−3x−y=4 .

Find the xxx - and yyy -intercepts of the line whose standard form is 3x+7y=−93 x+7 y=-93x+7y=−9 . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point (7,3)(7,3)(7,3) .

For each of the functions, determine the (i) domain (ii) range (iii) $x$ -intercept(s) (iv) $y$ -intercept(s). (a) (b) (c)

Use the figure to solve each equation or inequality. (a) $f(x)=g(x)$ (b) $f(x)<g(x)$ (c) $f(x) \geq g(x)$ (d) $y_{2}-y_{1}=0$ $Use the figure to solve each equation or inequality. (a) f(x)=g(x) (b) f(x)<g(x) (c) f(x) \geq g(x) (d) y_{2}-y_{1}=0$

Find the equation of the line passing through the point $(1,-4)$ and (a) parallel to the line with equation $y=2 x+3$ . (b) perpendicular to the line with equation $3 x+y=0$ .

Find the $x$ - and $y$ -intercepts of the line whose standard form is $-3 x+2 y=9$ . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point $(-2,12)$ .

Use the figure to solve each equation or inequality. (a) $f(x)=g(x)$ (b) $f(x)<g(x)$ (c) $f(x) \geq g(x)$ (d) $y_{2}-y_{1}=0$ $Use the figure to solve each equation or inequality. (a) f(x)=g(x) (b) f(x)<g(x) (c) f(x) \geq g(x) (d) y_{2}-y_{1}=0$

Find the equation of the line passing through the point $(2,-1)$ and (a) parallel to the line with equation $y=\frac{1}{2} x+3$ . (b) perpendicular to the line with equation $-3 x-y=4$ .

Find the $x$ - and $y$ -intercepts of the line whose standard form is $3 x+7 y=-9$ . What is the slope of this line?

Give the equations of both the horizontal and vertical lines passing through the point $(7,3)$ .