Q: Which of the following best describes the end behavior of $f(x) = -2x^4 + 3x^2 - 1$?

As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to -\infty$

Q: Which of the following describes the end behavior of $f(x) = x^5 - 2x^3 + x$?

As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$

Question 1

Which of the following describes the sequence of transformations needed to graph $h(x) = (x-2)^2 - 3$ using the parent function $f(x) = x^2$?

Accepted Answer

Shift the graph of $f(x)$ right 2 units and down 3 units.

Question 2

Given $f(x) = \sqrt{x+1}$, what is the domain of $f(x)$?

Accepted Answer

$[-1, \infty)$

Question 3

Suppose $g(x) = \dfrac{2x+1}{x-3}$. Which of the following statements is true about the graph of $g(x)$?

Accepted Answer

There is a vertical asymptote at $x = 3$ and a horizontal asymptote at $y = 2$

Question 4

A ball is thrown upward from a height of 8 feet. Its height after $x$ feet of horizontal distance is given by $h(x) = -0.02x^2 + 0.5x + 8$. What is the maximum height the ball reaches?

Accepted Answer

$9.25$ feet

Question 5

Given $f(x) = x^3 - 4x$, determine whether the function has a maximum or minimum value and state the value.

Accepted Answer

The function has neither a maximum nor a minimum value.

Question 6

Find the zeros of the polynomial $f(x) = x^3 - 4x^2 + 4x$.

Accepted Answer

$x = 0, 2, 2$

Question 7

Which of the following rational functions has a hole at $x = 2$?

Accepted Answer

$f(x) = \dfrac{x-2}{x^2-4}$

Question 8

Given $f(x) = x^2$ and $g(x) = x+1$, find $(f \circ g)(2)$.

Accepted Answer

$9$

Question 9

Which of the following best describes the end behavior of $f(x) = -2x^4 + 3x^2 - 1$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o -\infty$

Question 10

Given $f(x) = \sqrt{x-1}$, which of the following intervals represents the domain of $f(x)$?

Accepted Answer

$[1, \infty)$

Question 11

Which of the following is the inverse of $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \dfrac{x-5}{2}$

Question 12

A company’s profit per day by selling $x$ products is given by $P(x) = -0.01x^2 + 3.22x + 400$. How many products should be sold to maximize profit?

Accepted Answer

$161$

Question 13

Given $f(x) = x^2 - 4$ and $g(x) = x + 2$, find $(f + g)(-2)$.

Accepted Answer

$-2$

Question 14

Which of the following is NOT a polynomial function?

Accepted Answer

$f(x) = \dfrac{1}{x}$

Question 15

Find the horizontal asymptote of $f(x) = \dfrac{3x^2 + 1}{x^2 - 4}$.

Accepted Answer

$y = 3$

Question 16

Given $f(x) = x^2 - 4x + 3$, which of the following statements about its zeros is correct?

Accepted Answer

The zeros are $x = 1$ and $x = 3$.

Question 17

Which of the following best describes the symmetry of the function $f(x) = x^4$?

Accepted Answer

Even symmetry (about the $y$-axis)

Question 18

Given $f(x) = \dfrac{1}{x^2}$, which of the following is true about its domain?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 19

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

Accepted Answer

$(2x + 1)^2$

Question 20

Which of the following describes the end behavior of $f(x) = x^5 - 2x^3 + x$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o \infty$; as $x 	o -\infty$, $f(x) 	o -\infty$

College Algebra Study Guide: Functions, Graphs, Transformations, and Polynomial/Rational Analysis

Study Guide - Practice Questions

Study Guide - Flashcards