# Algebra 2 and Trigonometry

## 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.

Check back soon!

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.

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.
$$\{(1,1),(2,4),(3,9),(4,16)\}$$

Check back soon!

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.

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.
$$\{(-2,5),(-1,5),(0,5),(1,5),(2,5)\}$$

Check back soon!

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.

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.

Check back soon!

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.

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.

Check back soon!

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.

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.

Check back soon!

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.

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.
$$\{(x, y) : y=5-x\}$$

Check back soon!

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.

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.
$$\left\{(x, y) : y=-x^{2}+3 x-2\right\}$$

Check back soon!

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.

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.
$$\{(x, y) : y=|4-x|\}$$

Check back soon!

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.

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.
$$\{(x, y) : y=\sqrt{3-x}\}$$

Check back soon!

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.

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.
$$\left\{(x, y) : y=\frac{1}{x^{2}+1}\right\}$$

Check back soon!

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.

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.
$$\left\{(x, y) : y=\frac{x-5}{|x-3|}\right\}$$

Check back soon!

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.
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, $x .$