Question 1

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 2

Given the relation $$\{(0, 187), (1, 212), (2, 225), (2, 238)\}$$, what is the domain?

Accepted Answer

$$\{0, 1, 2\}$$

Question 3

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

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 4

Use the vertical line test to determine which graph below does NOT represent a function.

Accepted Answer

A circle centered at the origin.

Question 5

Let $$f(x) = x^2$ - 2x + 7. $$What is $$f(-5)$$?

Accepted Answer

$$42$$

Question 6

Given the graph of $$f(x) = (x+3)(x-1)(x-2) ($$see image 1), what are the $$x-$$intercepts?

Accepted Answer

$$x = -3, 1, 2$$

Question 7

For the function $$f(x) = 2x$$ and $$g(x) = 2x - 3$$, what is the vertical distance between their graphs at $$x = 1$$?

Accepted Answer

$$3$$

Question 8

Suppose the graph of $$y = f(x)$$ passes through the points $$(-2, 0)$$, $$(0, 2)$$, and $$(1, 3). $$What is the domain of $$f$$?

Accepted Answer

$$[-2, 1]$$

Question 9

Given the graph of $$y = f(x)$$ with a closed point at $$(1, -1)$$ and an open point at $$(-2, 2)$$, what is $$f(1)$$?

Accepted Answer

$$-1$$

Question 10

A real-world scenario: The T cell count in a patient with HIV is modeled by $$y = f(x)$$, where $$x is $$years after infection. If $$f(5) = 400$$, what does this mean?

Accepted Answer

After 5 years, the patient's T cell count is 400 per milliliter of blood.

Question 11

If $$f(x) = x^2$ and g(x$$) = $$x^2 + 4$, how does the graph of g(x$$)$$ relate to the graph of f(x$$)$$?

Accepted Answer

It is shifted 4 units up.

Question 12

Given the function $$f(x) = x^2$ - 2x + 7$$, what is $$f(x-1)$$?

Accepted Answer

$$(x-1)^2 - 2(x-1) + 7$

Question 13

Which of the following statements about intercepts is TRUE?

Accepted Answer

A function can have more than one $$x-$$intercept but at most one $$y-$$intercept.

Question 14

Given the graph of $$y = f(x)$$, how do you find the range?

Accepted Answer

Look for all the outputs on the $$y-$$axis that correspond to points on the graph.

Question 15

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

Accepted Answer

$$1$$

Question 16

Suppose $$f(x) is $$defined for $$x in$$ $$[-2, 1]$$ and $$f(-2) = 0$$, $$f(0) = 2$$, $$f(1) = 3. $$What is the range of $$f$$?

Accepted Answer

$$[0, 3]$$

Question 17

Given the function $$f(x) = x^2$ - 2x + 7$$, what is the value of $$x$$ for which $$f(x) = 8$$?

Accepted Answer

$$x = 3$$

Question 18

Which of the following is NOT a function?

Accepted Answer

A circle centered at the origin.

Question 19

If a graph passes the vertical line test, what does this indicate?

Accepted Answer

The graph represents a function.

Study Guide: Basics of Functions and Their Graphs (Precalculus)

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