Question 1

Given the function $$f(x) = 3x^2$ + 2x$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$6x + 2 + 3h$$

Question 2

If $$f(x) = \frac{2x - 5}{x + B}$$ and $$f(1) = 3$$, what is the value of $$B$$?

Accepted Answer

$$-4$$

Question 3

Find the domain of $$g(x) = \frac{\sqrt{x-3}}{x-21}. $$Write your answer in interval notation.

Accepted Answer

$$[3, 21) \cup (21, \infty)$$

Question 4

Given $$f(x) = \frac{x+3}{x+7}$$, which of the following is the $$x-$$intercept of $$f$$?

Accepted Answer

$$(3, 0)$$

Question 5

For the function $$f(x) = \frac{x+3}{x+7}$$, what is the domain of $$f$$?

Accepted Answer

$$x 
eq -7$$

Question 6

Suppose $$g(x) = -3x^2$ - 2x + 3. $$What is the average rate of change of $$g(x)$$ from $$x = 0 to$$ $$x = 2$$?

Accepted Answer

$$-15$$

Question 7

Given the piecewise function $$f(x) = \begin{cases} 7 & 0 \u003c x \leq 2 \ x^2$ & 0 \u003c x \u003c 3 \ x & x \geq 3 \end{cases}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(0, 3) \cup [3, \infty)$$

Question 8

Which graph represents $$y = -2(x - 5)^2$ + 4$$ after applying the sequence of transformations: shift right by 5, vertical stretch by 2, reflect over $$x-$$axis, and shift up by 4?

Accepted Answer

Graph of $$y = -2(x - 5)^2$ + 4$$

Question 9

If $$f(x) = x^2$ - x$$ and $$g(x) = \sqrt{x^2$ + 1}$$, which of the following is the correct domain for $$g(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 10

Given $$f(x) = \frac{2x-5}{x+B}$$ and $$f(1) = 3$$, which of the following steps correctly finds $$B$$?

Accepted Answer

Set $$\frac{2(1)-5}{1+B} = 3$$ and solve for $$B$$

Question 11

For $$g(x) = \frac{\sqrt{x-3}}{x-21}$$, which value of $$x$$ makes the denominator zero?

Accepted Answer

$$x = 21$$

Question 12

If $$f(x) = \frac{x+3}{x+7}$$, what is the $$y-$$intercept of $$f$$?

Accepted Answer

$$(0, \frac{3}{7})$$

Question 13

Suppose $$g(x) = -3x^2$ - 2x + 3$$ models the height (in meters) of a ball thrown downward from a building, where $$x is $$time in seconds. What does the average rate of change from $$x = 0 to$$ $$x = 2$$ represent in this context?

Accepted Answer

The ball's average velocity over the first 2 seconds

Question 14

Given $$f(x) = x^2$ - x$$, which of the following is the correct expression for $$f(x+h) - f(x)$$?

Accepted Answer

$$2xh + h^2$ - h$$

Question 15

For the function $$f(x) = \frac{x+3}{x+7}$$, which value of $$x$$ makes the function undefined?

Accepted Answer

$$x = -7$$

Question 16

If $$f(x) = x^2$ - x$$, what is the value of $$f(2)$$?

Accepted Answer

Question 17

Which transformation is NOT applied to $$y = x^2$ to obtain y$$ = $$-2(x-5)^2 + 4$?

Accepted Answer

Horizontal shift left by 5

Question 18

Given $$h(x) = x^2$ - x$$, what is the domain of $$h(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 19

If $$f(x) = \frac{2x-5}{x+B}$$ and $$f(1) = 3$$, what is the value of $$B$$ after solving $$\frac{2(1)-5}{1+B} = 3$$?

Accepted Answer

$$B = -4$$

Precalculus Practice: Functions, Domains, Transformations, and Piecewise Functions

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