Question 1

Which of the following graphs represents a function of $$x$$?

Accepted Answer

A parabola opening upwards

Question 2

Given the relation $$R = \{ (1,3), (2,6), (1,4), (3,0) \}$$, is $$R a $$function? What is its domain?

Accepted Answer

No; Domain: $$\{1,2,3\}$$

Question 3

Which of the following is the correct interval notation for the set $$\{ x \mid 2 \u003c x \leq 7 \}$$?

Accepted Answer

$$(2,7]$$

Question 4

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

Accepted Answer

$$f(-2) = 14$$

Question 5

Which of the following statements is TRUE about the function $$f(x) = x^2$?

Accepted Answer

It is an even function because $$f(-x) = f(x)$$

Question 6

Suppose the domain of a function $$f is$$ $$(-\infty, 5]. $$Which of the following is NOT in the domain?

Accepted Answer

$$x = 6$$

Question 7

Given $$g(x) = x^2$ + 5x - 1$$, find the difference quotient $$\frac{g(x+h) - g(x)}{h}$$ for $$h 
eq 0.$$

Accepted Answer

$$2x + h + 5$$

Question 8

A function is increasing on an interval if:

Accepted Answer

The $$y-$$values get bigger as the $$x-$$values get bigger

Question 9

Given $$f(x) = |x|$$, which of the following statements is correct?

Accepted Answer

The function is even

Question 10

If $$f(x) = 2x - 3$$, what is the value of $$x$$ for which $$f(x) = 7$$?

Accepted Answer

$$x = 5$$

Question 11

Which of the following is the range of the function $$f(x) = x^2$ + 1$$?

Accepted Answer

$$[1, \infty)$$

Question 12

Given the function $$f(x) = \sqrt{x-2}$$, what is its domain?

Accepted Answer

$$[2, \infty)$$

Question 13

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 14

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 15

Given $$f(x) = 2x^2$ - 8x + 6$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -2)$$

Question 16

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

Accepted Answer

The set of all possible output values

Question 17

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = -4.9t^2$ + 20t + 1.5$$, where $$t is $$time in seconds. What is the maximum height reached by the ball?

Accepted Answer

$$21.9$$ meters

Question 18

Given $$f(x) = x^2$ - 2x + 1$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$

Question 19

Which of the following is the correct set-builder notation for the interval $$(-\infty, 3]$$?

Accepted Answer

$$\{ x \mid x \leq 3 \}$$

Precalculus Study Notes: Functions, Domain & Range, Interval Notation, and More

Study Guide - Practice Questions

Study Guide - Flashcards