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Precalculus with Limits

Ron Larson

Chapter 1

Functions and Their Graphs - all with Video Answers

Educators

+ 21 more educators

Section 1

Rectangular Coordinates

00:53

Problem 1

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

TT
Troy Toth
Numerade Educator
03:11

Problem 2

The point of intersection of the $x$ - and $y$ -axes is the_____, and the two axes divide the coordinate plane into four parts called _____.

Anita Gordon
Anita Gordon
Numerade Educator
00:40

Problem 3

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

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
00:55

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
Suzana Milea
Numerade Educator
04:47

Problem 5

Plotting Points in the Cartesian Plane In
Exercises 5, plot the points in the Cartesian plane.
$$
(-4,2),(-3,-6),(0,5),(1,-4),(0,0),(3,1)
$$

Jimmy Yao
Jimmy Yao
Numerade Educator
07:32

Problem 6

Plotting Points in the Cartesian Plane In
Exercises 6, plot the points in the Cartesian plane.
$$
\left(1,-\frac{1}{3}\right),(0.5,-1),\left(\frac{3}{7}, 3\right),\left(-\frac{4}{3},-\frac{3}{7}\right),(-2,2.5)
$$

Chris Trentman
Chris Trentman
Numerade Educator
03:49

Problem 7

Finding the Coordinates of a Point In Exercises 7 and 8 , find the coordinates of the point. The point is located three units to the left of the $y$ -axis and four units above the $x$ -axis.

Oswaldo Jiménez
Oswaldo Jiménez
Numerade Educator
04:03

Problem 8

Finding the Coordinates of a Point In Exercises 8, find the coordinates of the point. The point is on the $x$ -axis and 12 units to the left of the $y$ -axis.

Karuna Ramroop
Karuna Ramroop
Numerade Educator
02:27

Problem 10

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is
located so that the condition(s) is (are) satisfied.
$$
x<0 \text { and } y<0
$$

US
Unique Snyder
Numerade Educator
00:28

Problem 11

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is
located so that the condition(s) is (are) satisfied.
$$
x=-4 \text { and } y>0
$$

Amanda Tricario
Amanda Tricario
Numerade Educator
00:54

Problem 12

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is
located so that the condition(s) is (are) satisfied.
$$
y<-5
$$

Karla Conrey
Karla Conrey
Numerade Educator
02:59

Problem 13

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is
located so that the condition(s) is (are) satisfied.
$$
x<0 \text { and }-y>0
$$

PM
Pranati Modumudi
Numerade Educator
02:55

Problem 14

Determining Quadrant(s) for a Point, determine the quadrant(s) in which $(x, y)$ is
located so that the condition(s) is (are) satisfied.
$$
x y>0
$$

Taylor Shimono
Taylor Shimono
Numerade Educator
02:00

Problem 15

Sketching a Scatter Plot In Exercises 15 and $16,$ sketch a scatter plot of the data shown in the table. The table shows the number $y$ of Wal-Mart stores for each year $x$ from 2003 through $2010 .$ (Source: Wal-Mart Stores, Inc.)

James Kiss
James Kiss
Numerade Educator
10:14

Problem 16

Sketching a Scatter Plot, sketch a scatter plot of the data shown in the table. 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 $)$

Chris Trentman
Chris Trentman
Numerade Educator
00:51

Problem 17

Finding a Distance In Exercises $17-22,$ find the distance between the points.
$$(-2,6),(3,-6)$$

Sujit Kumar
Sujit Kumar
Numerade Educator
01:44

Problem 18

Finding a Distance, find the distance between the points.
$$
(8,5),(0,20)
$$

AN
Aryan Narang
Numerade Educator
03:38

Problem 19

Finding a Distance, find the distance between the points.
$$
(1,4),(-5,-1)
$$

YS
Yoochan Shin
Numerade Educator
04:13

Problem 20

Finding a Distance, find the distance between the points.
$$
(1,3),(3,-2)
$$

Casey Castelli
Casey Castelli
Numerade Educator
03:10

Problem 21

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

Chris Trentman
Chris Trentman
Numerade Educator
07:05

Problem 22

Finding a Distance, find the distance between the points.
$$
(9.5,-2.6),(-3.9,8.2)
$$

Chris Trentman
Chris Trentman
Numerade Educator
05:50

Problem 23

Verifying a Right Triangle In Exercises 23,
(a) find the length of each side of the right triangle, and
(b) show that these lengths satisfy the Pythagorean Theorem.

YS
Yitzchak Shmalo
Numerade Educator
07:43

Problem 24

Verifying a Right Triangle In Exercises 24,
(a) find the length of each side of the right triangle, and
(b) show that these lengths satisfy the Pythagorean
Theorem.

Chris Trentman
Chris Trentman
Numerade Educator
05:14

Problem 25

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: $(4,0),(2,1),(-1,-5)$

RP
Raymond Purcell
Numerade Educator
10:21

Problem 26

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: $(-1,3),(3,5),(5,1)$

Chris Trentman
Chris Trentman
Numerade Educator
05:02

Problem 27

Verifying a Polygon, show that
the points form the vertices of the indicated polygon.
Isosceles triangle: $(1,-3),(3,2),(-2,4)$

Chris Trentman
Chris Trentman
Numerade Educator
06:48

Problem 28

Verifying a Polygon, show that
the points form the vertices of the indicated polygon.
Isosceles triangle: $(2,3),(4,9),(-2,7)$

Chris Trentman
Chris Trentman
Numerade Educator
04:49

Problem 29

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

Chris Trentman
Chris Trentman
Numerade Educator
04:20

Problem 30

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

Chris Trentman
Chris Trentman
Numerade Educator
05:49

Problem 31

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

Chris Trentman
Chris Trentman
Numerade Educator
05:37

Problem 32

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

Chris Trentman
Chris Trentman
Numerade Educator
04:38

Problem 33

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

Ashley Hanson
Ashley Hanson
Numerade Educator
06:26

Problem 34

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

Whitney Dillinger
Whitney Dillinger
Numerade Educator
09:37

Problem 35

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

Chris Trentman
Chris Trentman
Numerade Educator
04:08

Problem 36

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

Colleen Fontaine
Colleen Fontaine
Numerade Educator
06:41

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
Chris Trentman
Numerade Educator
05:24

Problem 38

Sports 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?

Chris Trentman
Chris Trentman
Numerade Educator
07:45

Problem 39

Sales 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
Chris Trentman
Numerade Educator
06:55

Problem 40

Earnings per Share 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.)

Chris Trentman
Chris Trentman
Numerade Educator
04:30

Problem 41

Translating Points in the Plane In Exercises 41,
find the coordinates of the vertices of the polygon after
the indicated translation to a new position in the plane.

Chris Trentman
Chris Trentman
Numerade Educator
03:49

Problem 42

Translating Points in the Plane In Exercises 42,
find the coordinates of the vertices of the polygon after
the indicated translation to a new position in the plane.

Chris Trentman
Chris Trentman
Numerade Educator
07:58

Problem 43

Translating Points in the Plane,
find the coordinates of the vertices of the polygon after
the indicated translation to a new position in the plane.
Original coordinates of vertices: $(-7,-2),(-2,2),$
$(-2,-4),(-7,-4)$
Shift: eight units up, four units to the right

Chris Trentman
Chris Trentman
Numerade Educator
08:47

Problem 44

Translating Points in the Plane,
find the coordinates of the vertices of the polygon after
the indicated translation to a new position in the plane.
Original coordinates of vertices: $(5,8),(3,6),(7,6)$
Shift: 6 units down, 10 units to the left

Chris Trentman
Chris Trentman
Numerade Educator
24:19

Problem 45

Minimum Wage 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
Chris Trentman
Numerade Educator
04:47

Problem 46

Data Analysis: Exam Scores 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.
$$
\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & {22} & {29} & {35} & {44} & {48} & {53} & {58} & {65} & {76} \\ \hline y & {53} & {74} & {57} & {66} & {79} & {90} & {76} & {93} & {99} \\ \hline\end{array}
$$
(a) Sketch a scatter plot of the data.
(b) Find the entrance test score of any student with a
final exam score in the 80s.
(c) Does a higher entrance test score imply a higher
final exam score? Explain.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:36

Problem 47

Using the Midpoint Formula 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 $y_{n m}$

Chris Trentman
Chris Trentman
Numerade Educator
05:35

Problem 48

Using the Midpoint Formula 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,
$$
\text { (a) }(1,-2),(4,-1) \text { and }\text { (b) }(-5,11),(2,4)
$$

Chris Trentman
Chris Trentman
Numerade Educator
View

Problem 49

Using the Midpoint Formula 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
10:13

Problem 50

Using the Midpoint Formula Use the result
of Exercise 49 to find the points that divide the line
segment joining the given points into four equal parts.
$$
(\mathrm{a})(1,-2),(4,-1) \quad \text { (b) }(-2,-3),(0,0)
$$

Chris Trentman
Chris Trentman
Numerade Educator
12:01

Problem 51

Make a Conjecture 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.

Chris Trentman
Chris Trentman
Numerade Educator
20:28

Problem 52

Collinear Points 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
Chris Trentman
Numerade Educator
01:54

Problem 53

Think About It 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
Yujie Wang
College of San Mateo
01:06

Problem 54

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

Carson Merrill
Carson Merrill
Numerade Educator
03:02

Problem 55

True or False? , determine whether
the statement is true or false. Justify your answer.
In order to divide a line segment into 16 equal parts, you
would have to use the Midpoint Formula 16 times.

Chris Trentman
Chris Trentman
Numerade Educator
04:55

Problem 56

True or False? , determine whether
the statement is true or false. Justify your answer.
The points $(-8,4),(2,11),$ and $(-5,1)$ represent the
vertices of an isosceles triangle.

Chris Trentman
Chris Trentman
Numerade Educator
15:05

Problem 57

True or False? , determine whether
the statement is true or false. Justify your answer.
If four points represent the vertices of a polygon, and
the four sides are equal, then the polygon must be a
square.

Chris Trentman
Chris Trentman
Numerade Educator
08:03

Problem 58

HOW DOYOU SEE IT? 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. IThe plots are
labeled (i), (ii), (iii), and (iv).]
$$
\begin{array}{ll}{\text { (a) }\left(x_{0}, y_{0}\right)} & {\text { (b) }\left(-2 x_{0}, y_{0}\right)} \\ {\text { (c) }\left(x_{0}, \frac{1}{2} y_{0}\right)} & {\text { (d) }\left(-x_{0},-y_{0}\right)}\end{array}
$$

Chris Trentman
Chris Trentman
Numerade Educator
01:37

Problem 59

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

Linda Hand
Linda Hand
Numerade Educator