Precalculus

Ron Larson

Chapter 1

Functions and Their Graphs - all with Video Answers

Educators

Section 1

Rectangular Coordinates

Problem 1

An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ________ plane.

ER

Eric Rethy

Numerade Educator

Problem 2

The point of intersection of the-and-axes is the ________, and the two axes divide the coordinate plane into four parts called ________.

Anita Gordon

Numerade Educator

Problem 3

The ________ ________ is a result derived from the Pythagorean Theorem.

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator

Problem 4

Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the ________ ________.

Suzana Milea

Numerade Educator

Problem 5

Plot the points in the Cartesian plane.
$$(-4,2),(-3,-6),(0,5),(1,-4),(0,0),(3,1)$$

James Kiss

Numerade Educator

Problem 6

Plot the points in the Cartesian plane.
$$\left(1,-\frac{1}{3}\right),(0.5,-1),\left(\frac{3}{7}, 3\right),\left(-\frac{4}{3},-\frac{3}{7}\right),(-2,2.5)$$

James Kiss

Numerade Educator

Problem 7

The point is located three units to the left of the $y$-axis and four units above the $x$-axis.

Massimo Antonelli

Massimo Antonelli

Numerade Educator

Problem 8

The point is on the $x$-axis and 12 units to the left of the $y$-axis.

Anas Venkitta

Numerade Educator

Problem 9

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$x>0$ and $y<0$

Karla Conrey

Numerade Educator

Problem 10

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$x<0$ and $y<0$

Amanda Tricario

Amanda Tricario

Numerade Educator

Problem 11

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$x=-4$ and $y>0$

Amanda Tricario

Amanda Tricario

Numerade Educator

Problem 12

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$$y<-5$$

Karla Conrey

Numerade Educator

Problem 13

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$$x<0 \text { and }-y>0$$

Karla Conrey

Numerade Educator

Problem 14

Determine the quadrant(s) in which $(x, y)$ is Iocated so that the condition(s) is (are) satisfied.
$$x y>0$$

Karla Conrey

Numerade Educator

Problem 15

The table shows the number $y$ of Wal-Mart stores for each year $x$ from 2003 through 2010. (Source: Wal-Mart Stores, Inc.
$$\begin{array}{|c|c|}\hline \text { Years, } x & \text { Number of Stores, } y\\\hline 2003 & 4906 \\2004 & 5289 \\2005 & 6141 \\2006 & 6779 \\2007 & 7262 \\2008 & 7720 \\2009 & 8416 \\2010 & 8970 \\\hline\end{array}$$

James Kiss

Numerade Educator

Problem 16

The table shows the lowest temperature on record $y$ (in degrees Fahrenheit) in Duluth, Minnesota, for each month $x,$ where $x=1$ represents January. (Source: NOAA)
$$\begin{array}{|c|c|}\hline \text { Month, } x & \text { Temperature, } y\\\hline 1 & -39 \\2 & -39 \\3 & -29 \\4 & -5 \\5 & 17 \\6 & 27 \\7 & 35 \\8 & 32 \\9 & 22 \\10 & 8 \\11 & -23 \\12 & -34 \\\hline\end{array}$$

Karla Conrey

Numerade Educator

Problem 17

Find the distance between the points.
$$(-2,6),(3,-6)$$

Anas Venkitta

Numerade Educator

Problem 18

Find the distance between the points.
$$(8,5),(0,20)$$

AN

Aryan Narang

Numerade Educator

Problem 19

Find the distance between the points.
$$(1,4),(-5,-1)$$

YS

Yoochan Shin

Numerade Educator

Problem 20

Find the distance between the points.
$$(1,3),(3,-2)$$

Casey Castelli

Numerade Educator

Problem 21

Find the distance between the points.
$$\left(\frac{1}{2}, \frac{4}{3}\right),(2,-1)$$

Chris Trentman

Numerade Educator

Problem 22

Find the distance between the points.
$$(9.5,-2.6),(-3.9,8.2)$$

Chris Trentman

Numerade Educator

Problem 23

(a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

Erika Bustos

Numerade Educator

Problem 24

(a) find the length of each side of the right triangle, and (b) show that these lengths satisfy the Pythagorean Theorem.

Erika Bustos

Numerade Educator

Problem 25

Show that the points form the vertices of the indicated polygon.
$$\text { Right triangle: }(4,0),(2,1),(-1,-5)$$

Anas Venkitta

Numerade Educator

Problem 26

Show that the points form the vertices of the indicated polygon.
$$\text { Right triangle: }(-1,3),(3,5),(5,1)$$

Anas Venkitta

Numerade Educator

Problem 27

Show that the points form the vertices of the indicated polygon.
$$\text { Isosceles triangle: }(1,-3),(3,2),(-2,4)$$

Anas Venkitta

Numerade Educator

Problem 28

Show that the points form the vertices of the indicated polygon.
$$\text { Isosceles triangle: }(2,3),(4,9),(-2,7)$$

Anas Venkitta

Numerade Educator

Problem 29

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(6,-3),(6,5)$$

Anas Venkitta

Numerade Educator

Problem 30

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(1,4),(8,4)$$

Anas Venkitta

Numerade Educator

Problem 31

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(1,1),(9,7)$$

Anas Venkitta

Numerade Educator

Problem 32

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(1,12),(6,0)$$

Anas Venkitta

Numerade Educator

Problem 33

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(-1,2),(5,4)$$

Anas Venkitta

Numerade Educator

Problem 34

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(2,10),(10,2)$$

Anas Venkitta

Numerade Educator

Problem 35

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$(-16.8,12.3),(5.6,4.9)$$

Anas Venkitta

Numerade Educator

Problem 36

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points.
$$\left(\frac{1}{2}, 1\right),\left(-\frac{5}{2}, \frac{4}{3}\right)$$

Anas Venkitta

Numerade Educator

Problem 37

An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers north and 150 kilometers west of Naples. How far does the plane fly?

Chris Trentman

Numerade Educator

Problem 38

A soccer player passes the ball from a point that is 18 yards from the endline and 12 yards from the sideline. A teammate who is 42 yards from the same endline and 50 yards from the same sideline receives the pass. (See figure.) How long is the pass?

Karla Conrey

Numerade Educator

Problem 39

The Coca-Cola Company had sales of $\$ 19,564$ million in 2002 and $\$ 35,123$ million in 2010. Use the Midpoint Formula to estimate the sales in 2006. Assume that the sales followed a linear pattern. (Source: The Coca-Cola Company)

Chris Trentman

Numerade Educator

Problem 40

The earnings per share for Big Lots, Inc. were $\$ 1.89$ in 2008 and $\$ 2.83$ in 2010 . Use the Midpoint Formula to estimate the earnings per share in $2009 .$ Assume that the earnings per share followed a linear pattern. (Source: Big Lots, Inc.)

JP

Joseph Proctor

Numerade Educator

Problem 41

Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.

Jonathan Ibarra

Jonathan Ibarra

Numerade Educator

Problem 42

Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.

Jonathan Ibarra

Jonathan Ibarra

Numerade Educator

Problem 43

Original coordinates of vertices: (-7,-2),(-2,2) (-2,-4),(-7,-4)
Shift: eight units up, four units to the right

Anas Venkitta

Numerade Educator

Problem 44

Original coordinates of vertices: (5,8),(3,6),(7,6)
Shift: 6 units down, 10 units to the left

Anas Venkitta

Numerade Educator

Problem 45

Use the graph below, which shows the minimum wages in the United States (in dollars) from 1950 through 2011 . (Source: U.S. Department of Labor)
(a) Which decade shows the greatest increase in minimum wage?
(b) Approximate the percent increases in the minimum wage from 1990 to 1995 and from 1995 to 2011 .
(c) Use the percent increase from 1995 to 2011 to predict the minimum wage in 2016
(d) Do you believe that your prediction in part (c) is reasonable? Explain.

Chris Trentman

Numerade Educator

Problem 46

The table shows the mathematics entrance test scores $x$ and the final examination scores $y$ in an algebra course for a sample of 10 students.
$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline x & 22 & 29 & 35 & 40 & 44 & 48 & 53 & 58 & 65 & 76 \\\hline y & 53 & 74 & 57 & 66 & 79 & 90 & 76 & 93 & 83 & 99 \\\hline\end{array}$$
(a) Sketch a scatter plot of the data.
(b) Find the entrance test score of any student with a final exam score in the $80 \mathrm{s}.$
(c) Does a higher entrance test score imply a higher final exam score? Explain.

Stephen Hobbs

Numerade Educator

Problem 47

A line segment has $\left(x_{1}, y_{1}\right)$ as one endpoint and $\left(x_{m}, y_{m}\right)$ as its midpoint. Find the other endpoint $\left(x_{2}, y_{2}\right)$ of the line segment in terms of $x_{1}, y_{1}, x_{m},$ and $y_{m}.$

Anas Venkitta

Numerade Educator

Problem 48

Use the result of Exercise 47 to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (a) (1,-2),(4,-1) and $(b)(-5,11),(2,4).$

James Kiss

Numerade Educator

Problem 49

Use the Midpoint Formula three times to find the three points that divide the line segment joining $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ into four parts.

ES

Elizabeth Streit

Numerade Educator

Problem 50

Use the result of Exercise 49 to find the points that divide the line segment joining the given points into four equal parts.
(a) (1,-2),(4,-1)
(b) (-2,-3),(0,0)

Yujie Wang

College of San Mateo

Problem 51

Plot the points (2,1),(-3,5) and (7,-3) on a rectangular coordinate system. Then change the signs of the indicated coordinates of each point and plot the three new points on the same rectangular coordinate system. Make a conjecture about the location of a point when each of the following occurs.
(a) The sign of the $x$-coordinate is changed.
(b) The sign of the $y$-coordinate is changed.
(c) The signs of both the $x$- and $y$-coordinates are changed.

Karla Conrey

Numerade Educator

Problem 52

Three or more points are collinear when they all lie on the same line. Use the steps following to determine whether the set of points $\{A(2,3), B(2,6), C(6,3)\}$ and the set of points $\{A(8,3)$ $B(5,2), C(2,1)\}$ are collinear.
(a) For each set of points, use the Distance Formula to find the distances from $A$ to $B$, from $B$ to $C$, and from $A$ to $C .$ What relationship exists among these distances for each set of points?
(b) Plot each set of points in the Cartesian plane. Do all the points of either set appear to lie on the same line?
(c) Compare your conclusions from part (a) with the conclusions you made from the graphs in part (b). Make a general statement about how to use the Distance Formula to determine collinearity.

Chris Trentman

Numerade Educator

Problem 53

When plotting points on the rectangular coordinate system, is it true that the scales on the $x$- and $y -axes must be the same? Explain.

Yujie Wang

College of San Mateo

Problem 54

What is the $y$-coordinate of any point on the $x$-axis? What is the $x$-coordinate of any point on the $y$-axis?

Anas Venkitta

Numerade Educator

Problem 55

In order to divide a line segment into 16 equal parts, you would have to use the Midpoint Formula 16 times.

Jonathon Brumley

Jonathon Brumley

Numerade Educator

Problem 56

The points $(-8,4),(2,11),$ and (-5,1) represent the vertices of an isosceles triangle.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 57

If four points represent the vertices of a polygon, and the four sides are equal, then the polygon must be a square.

Anna Jones

Numerade Educator

Problem 58

Use the plot of the point $\left(x_{0}, y_{0}\right)$ in the figure. Match the transformation of the point with the correct plot. Explain your reasoning. [The plots are labeled (i), (ii), (iii), and (iv).]
(a) $\left(x_{0}, y_{0}\right)$
(b) $\left(-2 x_{0}, y_{0}\right)$
(c) $\left(x_{0}, \frac{1}{2} y_{0}\right)$
(d) $\left(-x_{0},-y_{0}\right)$

James Kiss

Numerade Educator

Problem 59

Prove that the diagonals of the parallelogram in the figure intersect at their midpoints.

Harmender Singh Yadav

Harmender Singh Yadav

Numerade Educator