Q: What is the domain of the relation $$\{ (\text{Alex}, 9), (\text{Ellie}, 6), (\text{Nat}, 9), (\text{Grandma}, 70) \}$$?

$$\{ \text{Alex}, \text{Ellie}, \text{Nat}, \text{Grandma} \}$$

Question 1

Which of the following best describes a function from set $$X to $$set $$Y$$?

Accepted Answer

A relation that associates each element of $$X$$ with exactly one element of $$Y.$$

Question 2

Given the relation $$\{ (2,3), (4,1), (3,2), (2,1) \}$$, is this relation a function?

Accepted Answer

No, because the input $$2 is $$associated with two different outputs.

Question 3

What is the domain of the relation $$\{ (	ext{Alex}, 9), (	ext{Ellie}, 6), (	ext{Nat}, 9), (	ext{Grandma}, 70) \}$$?

Accepted Answer

$$\{ 	ext{Alex}, 	ext{Ellie}, 	ext{Nat}, 	ext{Grandma} \}$$

Question 4

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$y^2 + 8$$ = $$x^2$$

Question 5

If the relation pairs each animal with its appendage as follows: fish $$\rightarrow$$ fins, dog $$\rightarrow$$ legs, bird $$\rightarrow$$ legs and wings, is this relation a function?

Accepted Answer

No, because 'bird' is associated with two different appendages.

Question 6

Given the equation $$5x + 7y = 10$$, does this equation define $$y as a $$function of $$x$$?

Accepted Answer

Yes, because for each $$x$$ there is exactly one $$y$$ value.

Question 7

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible outputs (images) of the function.

Question 8

Consider the set of ordered pairs $$\{ (-2,3), (4,1), (3,-2), (2,1) \}. $$What is the range?

Accepted Answer

$$\{ 3, 1, -2 \}$$

Question 9

Which of the following real-world scenarios is NOT a function?

Accepted Answer

Assigning each person their possible shoe sizes.

Question 10

Given $$y^2 + 8$$ = $$x^2$$, why does this equation NOT define $$y as a $$function of $$x$$?

Accepted Answer

Because for some $$x$$ values, there are two possible $$y$$ values.

Question 11

Which of the following is a valid domain for the function $$y = 2x - 5$$?

Accepted Answer

All real numbers

Question 12

If a relation assigns the same output to multiple inputs, is it still a function?

Accepted Answer

Yes, as long as each input has only one output.

Question 13

Which of the following is the correct way to solve for $$y in$$ $$5x + 7y = 10$$?

Accepted Answer

$$y = -\frac{5}{7}x + \frac{10}{7}$$

Question 14

Which of the following is NOT a valid range for the relation $$\{ (2,3), (4,1), (3,2), (2,1) \}$$?

Accepted Answer

$$\{ 1, 2, 3, 4 \}$$

Question 15

A relation is given by the set $$\{ (a, 1), (b, 2), (c, 3), (a, 1) \}. Is $$this a function?

Accepted Answer

Yes, because each input is associated with exactly one output.

Functions: Definitions, Examples, and Determining Functionality

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