Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input has exactly one output.

Question 2

Given the set of ordered pairs $$\{(1,2), (2,3), (3,4), (2,5)\}$$, is this set a function?

Accepted Answer

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

Question 3

Which test can be used to determine if a graph represents a function?

Accepted Answer

Vertical line test

Question 4

If $$f(x) = 2x + 1$$, what is $$f(4)$$?

Accepted Answer

$$9$$

Question 5

Given $$f(x) = x^2$ + 2x$$, what is $$f(3)$$?

Accepted Answer

$$15$$

Question 6

Which of the following is the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$\{x \mid x 
eq 2\}$$

Question 7

A function $$f is $$defined as $$f(x) = x^2$. Which of the following statements is true?

Accepted Answer

The domain of $$f is $$all real numbers.

Question 8

If $$y = mx + b is a $$linear function, what does $$m$$ represent?

Accepted Answer

The slope

Question 9

Given the linear function $$y = 6x + 5$$, what is the y-intercept?

Accepted Answer

$$5$$

Question 10

A line passes through the point $$(2, 10)$$ and has a slope of $$6. $$What is its equation in the form $$y = mx + b$$?

Accepted Answer

Question 11

Which of the following is NOT a function?

Accepted Answer

A relation where $$f(2) = 3$$ and $$f(2) = 4$$

Question 12

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

Accepted Answer

Question 13

The function $$\pi(x)$$ counts the number of primes less than or equal to $$x. $$What is $$\pi(5)$$?

Accepted Answer

$$3$$

Question 14

If $$y = 9x + 18$$, what is the x-intercept?

Accepted Answer

$$-2$$

Question 15

Which of the following is the range of $$f(x) = x^2$ for x$$ \in \mathbb{R}$$?

Accepted Answer

$$\{y \mid y \geq 0\}$$

Question 16

If $$y = mx + b$$ and the line is parallel to $$y = 4x + 5$$, what is the slope of the parallel line?

Accepted Answer

$$4$$

Question 17

Given $$f(x) = x^2$ + 2x$$ and $$g(x) = x + 1$$, what is $$f(g(2))$$?

Accepted Answer

$$12$$

Question 18

If $$y = 6x + 5$$, what is the slope of the line?

Accepted Answer

$$6$$

Question 19

Which of the following is the correct formula for the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Functions and Linear Functions: Definitions, Properties, and Applications

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