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Precalculus: Functions and Graphs

Earl W. Swokowski, Jeffrey A. Cole

Chapter 2

Functions and Graphs - all with Video Answers

Educators

Section 1

Rectangular Coordinate Systems

03:21

Problem 1

Plot the points $A(5,-2), B(-5,-2), C(5,2), D(-5,2)$ $E(3,0),$ and $F(0,3)$ on a coordinate plane.

Raushan Kumar
Raushan Kumar
Numerade Educator
03:18

Problem 2

Plot the points $A(-3,1), B(3,1), C(-2,-3), D(0,3),$ and $E(2,-3)$ on a coordinate plane. Draw the line segments $A B$ $B C, C D, D E,$ and $E A$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:20

Problem 3

Plot the points $A(0,0), B(1,1), C(3,3), D(-1,-1),$ and $E(-2,-2) .$ Describe the set of all points of the form $(a, a),$ where $a$ is a real number.

Raushan Kumar
Raushan Kumar
Numerade Educator
03:23

Problem 4

Plot the points $A(0,0), B(1,-1), C(3,-3), D(-1,1)$ and $E(-3,3) .$ Describe the set of all points of the form $(a,-a),$ where $a$ is a real number.

Raushan Kumar
Raushan Kumar
Numerade Educator
02:24

Problem 5

Find the coordinates of the points $A-F$.
(GRAPH CAN NOT COPY)

Raushan Kumar
Raushan Kumar
Numerade Educator
02:03

Problem 6

Find the coordinates of the points $A-F$.
(GRAPH CAN NOT COPY)

Raushan Kumar
Raushan Kumar
Numerade Educator
04:39

Problem 7

Describe the set of all points $P(x, y)$ in a coordinate plane that satisfy the given condition.
(a) $x=-2$
(b) $y=3$
(c) $x \geq 0$
(d) $x y>0$
(e) $y<0$
(f) $x=0$

Raushan Kumar
Raushan Kumar
Numerade Educator
04:41

Problem 8

Describe the set of all points $P(x, y)$ in a coordinate plane that satisfy the given condition.
(a) $y=-2$
(b) $x=-4$
(c) $x / y<0$
(d) $x y=0$
(e) $y>1$
(f) $y=0$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:39

Problem 9

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(4,-3), \quad B(6,2)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:05

Problem 10

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(-2,-5), \quad B(4,6)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:47

Problem 11

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(-5,0), \quad B(-2,-2)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:31

Problem 12

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(6,2), \quad B(6,-2)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:32

Problem 13

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(7,-3), \quad B(3,-3)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:04

Problem 14

(a) Find the distance $d(A, B)$ between $A$ and $B$
(b) Find the midpoint of the segment $A B$
$$A(-4,7), \quad B(0,-8)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
05:04

Problem 15

Show that the triangle with vertices $A, B$, and $C$ is a right triangle, and find its area.
(GRAPH CAN NOT COPY)

Raushan Kumar
Raushan Kumar
Numerade Educator
04:38

Problem 16

Show that the triangle with vertices $A, B$, and $C$ is a right triangle, and find its area.
(GRAPH CAN NOT COPY)

Raushan Kumar
Raushan Kumar
Numerade Educator
03:25

Problem 17

Show that $A(-4,2), B(1,4), C(3,-1),$ and $D(-2,-3)$ are vertices of a square.

Raushan Kumar
Raushan Kumar
Numerade Educator
03:06

Problem 18

Show that $A(-4,-1), B(0,-2), C(6,1),$ and $D(2,2)$ are vertices of a parallelogram.

Raushan Kumar
Raushan Kumar
Numerade Educator
02:25

Problem 19

Given $A(-3,8),$ find the coordinates of the point $B$ such that $C(5,-10)$ is the midpoint of segment $A B$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:25

Problem 20

Given $A(5,-8)$ and $B(-6,2),$ find the point on segment $A B$ that is three-fourths of the way from $A$ to $B$.

Khushbu Rani
Khushbu Rani
Numerade Educator
01:45

Problem 21

Prove that $C$ is on the perpendicular bisector of segment $A B$
$$A(-4,-3), \quad B(6,1), \quad C(5,-11)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:39

Problem 22

Prove that $C$ is on the perpendicular bisector of segment $A B$
$$A(-3,2), \quad B(5,-4), \quad C(7,7)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:12

Problem 23

Find a formula that expresses the fact that an arbitrary point $P(x, y)$ is on the perpendicular bisector $l$ of segment $A B$
$$A(-4,-3), B(6,1)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
00:57

Problem 24

Find a formula that expresses the fact that an arbitrary point $P(x, y)$ is on the perpendicular bisector $l$ of segment $A B$
$$A(-3,2), B(5,-4)$$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:09

Problem 25

Find a formula that expresses the fact that $P(x, y)$ is a distance 5 from the origin. Describe the set of all such points.

Raushan Kumar
Raushan Kumar
Numerade Educator
02:52

Problem 26

Find a formula that states that $P(x, y)$ is a distance $r>0$ from a fixed point $C(h, k) .$ Describe the set of all such points.

Jill Tolbert
Jill Tolbert
Numerade Educator
02:19

Problem 27

Find all points on the $y$ -axis that are a distance 6 from $P(5,3)$

Raushan Kumar
Raushan Kumar
Numerade Educator
01:59

Problem 28

Find all points on the $x$ -axis that are a distance 5 from $P(-2,4)$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:42

Problem 29

Find the point with coordinates of the form $(2 a, a)$ that is in the third quadrant and is a distance 5 from $P(1,3)$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:34

Problem 30

Find all points with coordinates of the form $(a, a)$ that are a distance 3 from $P(-2,1)$

Raushan Kumar
Raushan Kumar
Numerade Educator
05:43

Problem 31

For what values of $a$ is the distance between $P(a, 3)$ and $Q(5,2 a)$ greater than $\sqrt{26} ?$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:38

Problem 32

Given $A(-2,0)$ and $B(2,0),$ find a formula not containing radicals that expresses the fact that the sum of the distances from $P(x, y)$ to $A$ and to $B,$ respectively, is 5

Aman Gupta
Aman Gupta
Numerade Educator
02:44

Problem 33

Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices. (Hint: Label the vertices of the triangle $O(0,0), A(a, 0), \text { and } B(0, b) .)$

Raushan Kumar
Raushan Kumar
Numerade Educator
03:30

Problem 34

Prove that the diagonals of any parallelogram bisect each other. (Hint: Label three of the vertices of the parallelogram $O(0,0), A(a, b), \text { and } C(0, c) .)$

Jill Tolbert
Jill Tolbert
Numerade Educator
00:42

Problem 35

Plot the points in the given viewing rectangle.
$$\begin{aligned}
&A(-5,-3.5), B(-2,2), C(1,0.5), D(4,1), \text { and } E(7,2.5) \text { in }\\
&[-10,10] \text { by }[-10,10]
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
01:06

Problem 36

Plot the points in the given viewing rectangle.
$$\begin{aligned}
&A(-10,4), \quad B(-7,-1.1), \quad C(0,-6), \quad D(3,-5.1), \quad \text { and }\\
&E(9,2.1) \text { in }[-12,12] \text { by }[-8,8]
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
01:17

Problem 37

The table lists the number of U.S. households with a computer for selected years.
$$\begin{array}{|l|l|}
\hline \text { Year } & \text { Households } \\
\hline 1997 & 36,600,000 \\
\hline 1998 & 42,100,000 \\
\hline 2000 & 51,000,000 \\
\hline 2001 & 56,300,000 \\
\hline 2003 & 61,800,000 \\
\hline
\end{array}$$
(a) Plot the data in the viewing rectangle $[1996,2004]$ by $\left[35 \times 10^{5}, 63 \times 10^{6}, 1 \times 10^{7}\right]$
(b) Discuss how the number of households is changing.

Erika Bustos
Erika Bustos
Numerade Educator
02:14

Problem 38

The table lists the number of daily newspapers published in the United States for various years.
(a) Plot the data in the viewing rectangle $[1895,2005,10]$ by $[0,3000,1000]$
(b) Use the midpoint formula to estimate the number of newspapers in $1930 .$ Compare your answer with the true value, which is 1942
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Newspapers } \\
\hline 1900 & 2226 \\
\hline 1920 & 2042 \\
\hline 1940 & 1878 \\
\hline 1960 & 1763 \\
\hline 1980 & 1745 \\
\hline 2000 & 1480 \\
\hline
\end{array}$$

Erika Bustos
Erika Bustos
Numerade Educator