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

I and 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{2}{x} - 3$$

Question 11

A company models its profit with $$P(x) = -2x^2$ + 8x - 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$3 at$$ $$x = 2$$

Question 12

A medication's concentration in the bloodstream is modeled by $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. After how many hours will the concentration drop to 1$ mg/L?

Accepted Answer

$$t = \frac{\ln(5)}{0.2}$$

Question 13

Which of the following describes the effect of replacing $$x$$ with $$x - 4 in $$the function $$f(x)$$?

Accepted Answer

Shifts the graph right by $$4$$ units

Question 14

Given $$h(x) = \sqrt{4 - x^2$}$$, what is the domain of $$h$$?

Accepted Answer

$$[-2, 2]$$

Question 15

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$

Question 16

A ball is thrown upward from a height of $$2$$ meters with an initial velocity of $$10 m/s. $$Its height after $$t$$ seconds is $$h(t) = -4.9t^2$ + 10t + 2. $$When does the ball reach its maximum height?

Accepted Answer

$$t = \frac{10}{9.8} s$$

Question 17

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = x + 1$$ and $$g(x) = x^2$?

Accepted Answer

$$(x + 1)^2$

Question 18

If $$f(x) is $$one-to-one and $$f(3) = 7$$, what is $$f^{-1}(7$$)$$?

Accepted Answer

$$3$$

Question 19

Which of the following best describes the graph of $$y = |x|$$?

Accepted Answer

A V-shaped graph with vertex at $$(0, 0)$$

Question 20

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

Accepted Answer

$$(x + 2)^2$

Precalculus Exam 2 Study Guidance

Study Guide - Practice Questions

Study Guide - Flashcards