$$\{x \mid x \neq 0, x \neq 3\}$$

Question 1

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

Accepted Answer

The set of all possible input values (x-coordinates)

Question 2

Given the relation $$\{(1,2), (2,3), (3,4), (2,5)\}$$, is this relation a function?

Accepted Answer

No, because the input 2 is paired with two different outputs

Question 3

For the function $$f(x) = \sqrt{3x - 2}$$, what is the domain?

Accepted Answer

$$[\frac{2}{3}, \infty)$$

Question 4

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 5

A function $$f is $$defined by $$f(x) = -3x^2$ + 2x. $$What is $$f(-1)$$?

Accepted Answer

$$1$$

Question 6

If $$g(x) = x^2$ - 5x$$ and $$h(x) = 2x + 3$$, what is $$(g+h)(x)$$?

Accepted Answer

$$x^2 - 5x + 2x + 3$

Question 7

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

Question 8

A rectangle has a perimeter $$P = 2l + 2w = 100. $$Express the area $$A as a $$function of $$w$$ and find its domain.

Accepted Answer

$$A(w) = (50-w)w$$, \quad w \in (0,50)$

Question 9

Which of the following is written in implicit form?

Accepted Answer

$$3x + y = 5$$

Question 10

Given $$f(x) = \frac{x+4}{x^2$-3x}$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \mid x 
eq 0, x 
eq 3\}$$

Question 11

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

Accepted Answer

$$\{x \mid x 
eq -2\}$$

Question 12

Which statement about functions is TRUE?

Accepted Answer

A function assigns exactly one output to each input

Question 13

For $$f(x) = x^2$ - 2x + 1$$, what is $$f(2)$$?

Accepted Answer

$$-1$$

Question 14

Which of the following is the correct set-builder notation for the domain of $$g(x) = \frac{1}{x-4}$$?

Accepted Answer

$$\{x \mid x 
eq 4\}$$

Question 15

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

Accepted Answer

$$12$$

Question 16

Which of the following is the correct difference function $$f-g$$ for $$f(x) = x^2$ and g(x) = 2x$?

Accepted Answer

$$x^2 - 2x$

Question 17

A function $$f is $$defined by $$f(x) = \sqrt{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$[3, \infty)$$

Question 18

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

Accepted Answer

The set of all possible output values

Question 19

If $$f(x) = x^2$ and g(x) = x+2$, what is $$\left(\frac{f}{g}\right)(4)$$?

Accepted Answer

$$\frac{16}{6}$$

Functions and Their Graphs: Precalculus Study Notes

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