Question 1

Given the relation $$\{(soccer, 400), (basketball, 500), (swimming, 600), (soccer, 450)\}$$, what is the domain of this relation?

Accepted Answer

$$\{soccer, basketball, swimming\}$$

Question 2

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1, 2), (3, 4), (5, 6)\}$$

Question 3

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(2)$$?

Accepted Answer

Question 4

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain corresponds to exactly one element in the range.

Question 5

Given the function $$g(x) = 3x^2$ - 10$$, what is $$g(-2)$$?

Accepted Answer

$$2$$

Question 6

A table shows the following values for $$h(x)$$: $$h(0) = 5$$, $$h(1) = 7$$, $$h(2) = 9$$, $$h(3) = 11. $$What is the range of $$h$$?

Accepted Answer

$$\{5, 7, 9, 11\}$$

Question 7

Which of the following real-life scenarios is best modeled by a function?

Accepted Answer

Each student in a class is assigned to one locker.

Question 8

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

Accepted Answer

No, because 'a' in the domain corresponds to more than one element in the range.

Question 9

If $$f(x) = 4x + 5$$, what is $$f(6)$$?

Accepted Answer

$$29$$

Question 10

Suppose $$g(x) is $$defined by the table: $$g(0) = 3$$, $$g(1) = 0$$, $$g(2) = 1$$, $$g(3) = 2$$, $$g(4) = 3. $$For which $$x$$ does $$g(x) = 3$$?

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 11

A fitness app records the calories burned per hour for different activities: $$\{(yoga, 200), (running, 600), (cycling, 400), (yoga, 250)\}. Is $$this relation a function?

Accepted Answer

No, because 'yoga' corresponds to more than one calorie value.

Question 12

If $$f(x) = x^2$ - 2x + 1$$, what is $$f(-3)$$?

Accepted Answer

$$16$$

Question 13

Which of the following is NOT a function?

Accepted Answer

$$\{(x, y), (x, z), (y, z)\}$$

Question 14

A hospital assigns each patient a unique medical record number. Which mathematical concept best describes this assignment?

Accepted Answer

A function from patients to medical record numbers.

Question 15

If $$h(x) = 2x - 7$$, and $$h(a) = -1$$, what is the value of $$a$$?

Accepted Answer

$$a = 3$$

Functions and Linear Functions: Foundations and Evaluation

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