Question 1

Which of the following is the correct domain in interval notation for the function $$f(x) = \sqrt{3x + 6}$$?

Accepted Answer

$$[-2, \infty)$$

Question 2

Given the function $$g(x) = \frac{1}{2x - 3}$$, which value is NOT in the domain of $$g(x)$$?

Accepted Answer

$$x = \frac{3}{2}$$

Question 3

Which of the following functions is even?

Accepted Answer

$$g(x) = x^4$ - 3$$

Question 4

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

Accepted Answer

The graph is symmetric with respect to the y-axis.

Question 5

Given $$f(x) = 5x + 7$$ and $$g(x) = 3x^2$ - 8$$, what is $$(f + g)(x)$$?

Accepted Answer

$$3x^2 + 5x - 1$

Question 6

Which of the following describes the transformation for $$f(x) = (\frac{1}{2}x)^2$ - 3$$ compared to $$f(x) = x^2$?

Accepted Answer

Horizontally stretched by 2 and shifted down 3

Question 7

For the piecewise function $$g(x) = \begin{cases} -2x - 1 & 	ext{if } x \u003e -2 \ x + 2 & 	ext{if } x \leq -2 \end{cases}$$, what is $$g(-7)$$?

Accepted Answer

$$-5$$

Question 8

Given $$f(x) = 5x + 7$$ and $$g(x) = 3x^2$ - 8$$, what is $$(f \circ g)(-1)$$?

Accepted Answer

$$-18$$

Question 9

If a ball is dropped from a 600-meter-tall building, and the time to fall $$d$$ meters is $$t(d) = \sqrt{\frac{d}{5}}$$, how long will it take to hit the ground? (Round to the nearest second.)

Accepted Answer

$$11$$ seconds

Question 10

Which of the following intervals correctly describes where the function $$f(x) is $$increasing if $$f(x)$$ has a relative minimum at $$x = -3$$ and a relative maximum at $$x = 4$$?

Accepted Answer

$$(-3, 4)$$

Question 11

Given $$k(x) = x^2$ - 3$$, find the difference quotient $$\frac{k(x+h) - k(x)}{h}.$$

Accepted Answer

$$2x + h$$

Question 12

Which of the following is the range of $$f(x) = 2$$?

Accepted Answer

$$\{2\}$$

Question 13

If $$f(x) = \sqrt{6 - x}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, 6]$$

Question 14

Which of the following is the correct composition $$(g \circ f)(x)$$ for $$f(x) = 5x + 7$$ and $$g(x) = 3x^2$ - 8$$?

Accepted Answer

$$75x^2 + 210x + 139$

Question 15

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 16

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

Accepted Answer

The function is odd.

Question 17

For the function $$f(x) = \sqrt{x^2$ - 4}$$, what is the domain?

Accepted Answer

$$(-\infty, -2) \cup (2, \infty)$$

Question 18

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

Accepted Answer

Question 19

A dropped object falls according to $$h = 16t^2$. How far has it fallen after t = 1.6$ seconds?

Accepted Answer

$$40.96$$ feet

Blank Coordinate Plane Grids for Graphing Functions

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