Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{4 - x^2$}$$?

Accepted Answer

$$[-2, 2]$$

Question 2

A function $$f is $$defined by $$f(x) = |x - 3| + 2. $$What is the range of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 3

Which of the following equations represents a function whose graph is symmetric about the y-axis?

Accepted Answer

$$y = x^2$

Question 4

Given $$f(x) = x^2$ + 1$$ and $$g(x) = \frac{1}{x}$$, what is the domain of the composition $$(f \circ g)(x)$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 5

A ball is dropped from a height of 100 ft. Its height at time $$t$$ seconds is $$s(t) = -16t^2$ + 100. $$What is the time when the ball hits the ground?

Accepted Answer

$$t = 6.25$$ seconds

Question 6

Which of the following is NOT a function?

Accepted Answer

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

Question 7

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

Accepted Answer

$$(f + g)(x) = 2x - 3 + x^2$ - 1$$, domain: $$(-\infty, \infty)$$

Question 8

Which of the following best describes the range of $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 9

A piecewise function is defined as $$f(x) = \begin{cases} -x, & x \u003c 0 \ x, & x \geq 0 \end{cases}. $$What is $$f(-3)$$ and $$f(2)$$?

Accepted Answer

$$f(-3) = 3, f(2) = 2$$

Question 10

Which of the following is the correct interpretation of the slope $$m in $$the linear equation $$y = mx + b in a $$real-world context?

Accepted Answer

The rate of change of $$y$$ with respect to $$x$$

Question 11

Which of the following is a transcendental function?

Accepted Answer

$$f(x) = \sin(x)$$

Question 12

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

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 13

Which of the following intervals is closed?

Accepted Answer

$$[a, b]$$

Question 14

If $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

$$f is an $$odd function

Question 15

Which of the following best describes the range of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 16

Suppose $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$. What is the domain of (f$$ \cdot g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 17

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

Accepted Answer

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

Question 18

Which of the following is the correct domain for the function $$f(x) = \frac{3}{x^2$ - 1}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, 1) \cup (1, \infty)$$

Question 19

If $$f(x) = x^2$ + 1$$ and $$g(x) = \frac{1}{x}$$, what is the range of $$(g \circ f)(x)$$?

Accepted Answer

College Algebra Study Guide: Functions and Their Properties

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