Question 1

Which of the following best describes the domain of the function $$y = \frac{1}{x+3}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, \infty)$$

Question 2

Given $$y = 2 - x^2$, which of the following statements is true?

Accepted Answer

The range is $$(-\infty, 2]$$

Question 3

For the function $$y = 9 - x^2$, what are the x$-intercepts?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 4

Which of the following functions is even?

Accepted Answer

$$f(x) = x^4$ - 6x^2$

Question 5

Consider the function $$f(x) = x^3$ + 6. $$Which of the following best describes its symmetry?

Accepted Answer

It is odd.

Question 6

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

Accepted Answer

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

Question 7

Which of the following is the correct domain for $$y = \sqrt{6 - 2x}$$?

Accepted Answer

$$(-\infty, 3]$$

Question 8

Given the piecewise function $$g(x) = \begin{cases} x^2$ + 1 & x \u003e 0 \ -x - 2 & -2 \u003c x \leq 0 \ x + 1 & x \leq -2 \end{cases}$$, on which interval is $$g(x)$$ decreasing?

Accepted Answer

$$-2 \u003c x \leq 0$$

Question 9

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x^2$ - 3x + 1$$

Question 10

Given $$y = x^2$ + 2$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 2)$$

Question 11

Which of the following best describes the range of $$y = -x^2$ + 7x - 6$$?

Accepted Answer

$$(-\infty, \frac{13}{4}]$$

Question 12

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

Accepted Answer

$$(x - 3)^2$ - 2$$

Question 13

Which of the following is a possible decomposition for $$j(x) = \frac{4x}{3} + 1 as$$ $$j(x) = p(s(x))$$?

Accepted Answer

$$p(x) = x + 1$$, $$s(x) = \frac{4x}{3}$$

Question 14

Which of the following equations is symmetric about the $$y-$$axis?

Accepted Answer

$$y = x^2$ + 5$$

Question 15

Given $$y = \frac{6}{x-5} - 6$$, which of the following is NOT true?

Accepted Answer

The function is defined for all real $$x$$

Question 16

For the function $$y = x^2$ + 2$$, which of the following is true about its zeros?

Accepted Answer

It has no real zeros.

Question 17

Given $$f(x) = x^2$ - 2$$ and $$h(x) = 1 - x^2$, what is the domain of (f$$ \circ h)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

Which of the following best describes the range of $$y = x^2$ + 2$$?

Accepted Answer

$$[2, \infty)$$

Question 19

Which of the following is the $$x-$$intercept of $$y = 4x - 3$$?

Accepted Answer

$$(\frac{3}{4}, 0)$$

Calculus 1-H: Pre-Calculus Practice Guidance

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