Question 1

Which of the following statements best describes the domain of the function $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

All real numbers $$x$$ such that $$x \geq 3$$

Question 2

Given the equation $$y = 4 - x^2$, what are the x$-intercepts of the graph?

Accepted Answer

$$x = \pm 2$$

Question 3

Which of the following sets represents the range of the function $$f(x) = x^2$ for x$$ \in [-2, 2]$$?

Accepted Answer

$$[0, 4]$$

Question 4

A relation is defined as $$R = \{(1, 2), (2, 3), (1, 4)\}. Is$$ $$R a $$function?

Accepted Answer

No, because the domain value $$1$$ corresponds to two different range values

Question 5

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(x + h)$$?

Accepted Answer

$$(x + h)^2$ - 4(x + h) + 7$$

Question 6

Which of the following is NOT a valid method to determine if a graph represents a function?

Accepted Answer

Looking for repeated $$y-$$values

Question 7

For the function $$g(x) = -x^2$ + 4x + 1$$, what is $$g(x + 2)$$?

Accepted Answer

$$-(x + 2)^2$ + 4(x + 2) + 1$$

Question 8

Which of the following intervals represents a domain where endpoints are included?

Accepted Answer

$$[a, b]$$

Question 9

A medical researcher models the spread of a virus with $$V(t) = 100e$$^{0.05t}$$, where t$ is days since outbreak. What is the range of V(t$$)$$?

Accepted Answer

$$[100, \infty)$$

Question 10

If $$f(x) = \frac{1}{x - 2}$$, which value is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 11

A function $$f is $$defined by $$f(x) = x^2$ - 4x + 7. $$What is $$f(-x)$$?

Accepted Answer

$$x^2 + 4x + 7$

Question 12

Which of the following best describes the range of $$f(x) = \sqrt{x}$$ for $$x \in [0, 9]$$?

Accepted Answer

$$[0, 3]$$

Question 13

A chemical reaction is modeled by $$C(t) = 5t^2$ - 3t + 2. $$What is $$C(2)$$?

Accepted Answer

$$12$$

Question 14

Which of the following is the correct set-builder notation for the domain $$[1, 4]$$?

Accepted Answer

$$\{x \mid 1 \leq x \leq 4\}$$

Question 15

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

Accepted Answer

Each $$x-$$value corresponds to exactly one $$y-$$value

Question 16

A function $$f is $$defined as $$f(x) = x^2$ - 4x + 7. $$What is the value of $$f(3)$$?

Accepted Answer

Question 17

Which of the following is NOT a function?

Accepted Answer

$$R = \{(1, 2), (1, 3)\}$$

Question 18

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(x - 2)$$?

Accepted Answer

$$(x - 2)^2$ - 4(x - 2) + 7$$

Question 19

A function $$f is $$defined as $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$[-3, 3]$$

Question 20

Which of the following best describes the range of $$f(x) = x^2$ for x$$ \in (-\infty, \infty)$$?

Accepted Answer

$$[0, \infty)$$

Precalculus Study Notes: Functions, Graphs, and Algebraic Foundations

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