Question 1

Let $$f(x) = -x^2$ - x. $$What is $$f(-a)$$?

Accepted Answer

$$-a^2 - a$

Question 2

Find the $$x-$$intercepts for $$g(x) = x^3$ - x.$$

Accepted Answer

III: $$(0, 0)$$, $$(1, 0)$$, and $$(-1, 0)$$

Question 3

Which of the following are functions?
I. $$x^2 - y = 1$
II. y^2$ - x = 1$$
III. $$y - x = 1
IV$$. $$y^2$$ - $$x^2 = 1$

Accepted Answer

III only

Question 4

Suppose we perform the following transformations to the graph of $$f in $$the indicated order:
1. reflection over the $$y-$$axis
2. vertical stretch by a factor of $$3
3. $$shift down $$2$$ units
What is the equation of the transformed graph?

Accepted Answer

$$g(x) = 3f(-x) - 2$$

Question 5

Suppose we perform the following transformations to the graph of $$f(x) = |x| in $$the indicated order:
1. shift left $$2$$ units
2. reflection over the $$x-$$axis
3. vertical stretch by a factor of $$3
4. $$shift up $$1$$ unit
What is the equation of the transformed graph?

Accepted Answer

$$g(x) = -3|x + 2| + 1$$

Question 6

Which of the following points on a graph are NOT moved by a horizontal reflection? Select all that apply.

Accepted Answer

$$(0, 0)$$

Question 7

What is the domain of $$f(x) = \frac{x}{\sqrt{1 - x}}$$?

Accepted Answer

$$(-\infty, 1]$$

Question 8

Let $$f(x) = x^2$ and g(x$$) = \sqrt{x - 1}$$. What is the domain of f$$ \circ g$$?

Accepted Answer

$$[1, \infty)$$

Question 9

Let $$f(x) = \frac{x}{x - 1}$$ and $$g(x) = \frac{2}{x}. $$Find $$(f \circ g)(x)$$ and simplify.

Accepted Answer

$$\frac{2}{2 - x}$$

Question 10

Find the inverse of $$f(x) = \frac{2}{x + 3}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{2x - 3}{x}$$

Question 11

A pharmaceutical company models the concentration of a drug in the bloodstream as $$C(t) = \frac{t}{\sqrt{1 - t}}$$, where $$t is $$time in hours. What is the maximum time $$t$$ for which the concentration is defined?

Accepted Answer

$$t \u003c 1$$

Question 12

A population growth model is given by $$P(x) = x^3$ - x. If $$the population is zero, what are the possible values of $$x$$?

Accepted Answer

$$x = 0, 1, -1$$

Question 13

Which of the following equations represents a function that could model the height of a projectile as a function of time?

Accepted Answer

$$y - x = 1$$

Question 14

A company wants to transform the cost function $$C(x) by $$reflecting it over the $$y-$$axis, stretching it vertically by $$3$$, and shifting it down $$2$$ units. What is the new cost function?

Accepted Answer

$$3C(-x) - 2$$

Question 15

If $$f(x) = |x|$$ models the distance from a starting point, and you shift the graph left $$2$$ units, reflect over the $$x-$$axis, stretch vertically by $$3$$, and shift up $$1$$ unit, what is the new function?

Accepted Answer

$$-3|x + 2| + 1$$

Question 16

Which points on the graph of $$y = x^2$ remain unchanged after a horizontal reflection?

Accepted Answer

$$(0, 0)$$

Question 17

Given $$f(x) = \frac{x}{x - 1}$$ and $$g(x) = \frac{2}{x}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x 
eq 0$$ and $$x 
eq 2$$

Question 18

If $$f(x) = \frac{2}{x + 3}$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$x 
eq 0$$

Precalculus Exam 2: Step-by-Step Study Guidance

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