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Algebra 2 and Trigonometry

Ann Xavier Gantert

Chapter 4

RELATIONS AND FUNCTIONS

Educators


Problem 1

Explain why $\left\{(x, y) : x=y^{2}\right\}$ is not a function but $\{(x, y) : \sqrt{x}=y\}$ is a function.

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Problem 2

Can $y=\sqrt{x}$ define a function from the set of positive integers to the set of positive integers? Explain why or why not.

Emma C.
Numerade Educator

Problem 3

In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range.
$$
\{(1,1),(2,4),(3,9),(4,16)\}
$$

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Problem 4

In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range.
$$
\{(1,-1),(0,0),(1,1)\}
$$

Emma C.
Numerade Educator

Problem 5

In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range.
$$
\{(-2,5),(-1,5),(0,5),(1,5),(2,5)\}
$$

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Problem 6

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

Emma C.
Numerade Educator

Problem 7

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

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Problem 8

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

Emma C.
Numerade Educator

Problem 9

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

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Problem 10

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

Emma C.
Numerade Educator

Problem 11

In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.

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Problem 12

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\{(x, y) : y=-183\}
$$

Emma C.
Numerade Educator

Problem 13

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\{(x, y) : y=5-x\}
$$

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Problem 14

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=x^{2}\right\}
$$

Emma C.
Numerade Educator

Problem 15

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=-x^{2}+3 x-2\right\}
$$

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Problem 16

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\{(x, y) : y=\sqrt{2 x}\}
$$

Emma C.
Numerade Educator

Problem 17

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\{(x, y) : y=|4-x|\}
$$

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Problem 18

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=\frac{1}{x}\right\}
$$

Emma C.
Numerade Educator

Problem 19

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\{(x, y) : y=\sqrt{3-x}\}
$$

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Problem 20

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=\frac{1}{\sqrt{x+1}}\right\}
$$

Emma C.
Numerade Educator

Problem 21

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=\frac{1}{x^{2}+1}\right\}
$$

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Problem 22

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=\frac{x+1}{x-1}\right\}
$$

Emma C.
Numerade Educator

Problem 23

In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer.
$$
\left\{(x, y) : y=\frac{x-5}{|x-3|}\right\}
$$

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Problem 24

The perimeter of a rectangle is 12 meters.
a. If $x$ is the length of the rectangle and $y$ is the area, describe, in set-builder notation, the area as a function of length.
b. Use integral values of $x$ from 0 to 10 and find the corresponding values of $y .$ Sketch the graph of the function.
c. What is the largest subset of the real numbers that can be the domain of the function?

Emma C.
Numerade Educator

Problem 25

A candy store sells candy by the piece for 10 cents each. The amount that a customer pays for candy, $y,$ is a function of the number of pieces purchased, $x .$
a. Describe, in set-builder notation, the cost in cents of each purchase as a function of the number of pieces of candy purchased.
b. Yesterday, no customer purchased more than 8 pieces of candy. List the ordered pairs that describe possible purchases yesterday.
c. What is the domain for yesterday's purchases?
d. What is the range for yesterday's purchases?

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