Question 1

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

Accepted Answer

$$7$$

Question 2

If $$f(x) = \frac{1-3x}{2}$$, what is $$f(2)$$?

Accepted Answer

$$-2$$

Question 3

For $$f(x) = 5 - 2x$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$-2$$

Question 4

Find the domain of $$f(x) = \frac{x}{x-3}.$$

Accepted Answer

$$x 
eq 3$$

Question 5

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = x^2$

Question 6

Given the graph of $$y = |x| + 1$$, which statement is true?

Accepted Answer

The graph is a function of $$x.$$

Question 7

For $$f(x) = x^2$, determine whether the function is even, odd, or neither.

Accepted Answer

Even

Question 8

If $$f(x) = x^3$ - x$$, is $$f(x)$$ even, odd, or neither?

Accepted Answer

Odd

Question 9

Which transformation describes $$y = (x-2)^2$ + 1$$ compared to $$y = x^2$?

Accepted Answer

Horizontal translation 2 units right, vertical translation 1 unit up

Question 10

Given the graph of a function, how do you find the interval where it is increasing?

Accepted Answer

Identify where the graph moves upward as $$x$$ increases.

Question 11

For $$f(x) = x^2$, what is the local minimum value and at which x$ does it occur?

Accepted Answer

Local minimum at $$x = 0$$, value $$0$$

Question 12

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

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 13

Which of the following is NOT a function?

Accepted Answer

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

Question 14

For $$f(x) = x^2$, what is f(x+h$$)$$?

Accepted Answer

$$(x+h)^2$$

Question 15

If $$f(x) = x^2$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 16

Which graph passes the vertical line test?

Accepted Answer

A parabola opening upwards

Question 17

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

Accepted Answer

$$x^2$$

Question 18

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

Accepted Answer

$$-x^3$$

Question 19

Which transformation describes $$y = (x+1)^2$ - 2$$ compared to $$y = x^2$?

Accepted Answer

Horizontal translation 1 unit left, vertical translation 2 units down

Functions and Their Properties: College Algebra Review

Study Guide - Practice Questions