It touches the $x$-axis at $x = 2$

Question 1

Which of the following is the correct domain of the function $k(x) = \sqrt{\dfrac{x}{x+2}}$?

Accepted Answer

$x \geq 0$ and $x + 2 > 0$

Question 2

Given the polynomial $f(x) = x^4 + x^3 + x^2 + x - 15$, which of the following is a possible rational zero according to the Rational Root Theorem?

Accepted Answer

$\pm 1$

Question 3

Let $R(x) = \dfrac{4x}{x-2}$. What is the equation of the vertical asymptote?

Accepted Answer

$x = 2$

Question 4

If $f(x) = x^2 - 6x + 9$, which transformation of $y = x^2$ produces $f(x)$?

Accepted Answer

Shift right 3 units

Question 5

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

Accepted Answer

$x \in \mathbb{R}$

Question 6

Which of the following is the correct inverse of $f(x) = 2x + 1$?

Accepted Answer

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

Question 7

Solve for $x$: $2^{x+1} = 32$

Accepted Answer

$x = 4$

Question 8

Which of the following is the correct simplified form of $\ln(7) + \ln(16)$?

Accepted Answer

$\ln(112)$

Question 9

Given $f(x) = x^2 - 5x + 6$, which of the following statements about its zeros is correct?

Accepted Answer

It has two real zeros at $x = 2$ and $x = 3$

Question 10

What is the horizontal asymptote of $R(x) = \dfrac{4x}{x-2}$?

Accepted Answer

$y = 1$

Question 11

If $f(x) = x^3 - 4x^2 + 4x$, which of the following is a factor of $f(x)$?

Accepted Answer

$x - 2$

Question 12

Find the domain of $f(x) = \ln(x^2 - 1)$.

Accepted Answer

$x > 1$ or $x < -1$

Question 13

Which of the following is the correct solution to $\log_2(x) + \log_2(x-1) = 1$?

Accepted Answer

$x = 3$

Question 14

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

Accepted Answer

$(x + 1)^2$

Question 15

Which of the following is the correct simplified form of $\log_2(8) - \log_2(4)$?

Accepted Answer

$\log_2(2)$

Question 16

If $f(x) = x^2 - 4$ and $g(x) = \sqrt{x}$, what is the domain of $(g \circ f)(x)$?

Accepted Answer

$x \leq -2$ or $x \geq 2$

Question 17

Which of the following is the correct solution to $\left(\dfrac{1}{3}\right)^x = 27$?

Accepted Answer

$x = -4$

Question 18

Given $f(x) = x^2 - 4x + 4$, which statement about its graph is correct?

Accepted Answer

It touches the $x$-axis at $x = 2$

Question 19

Which of the following is the correct simplified form of $\ln\left(\dfrac{7x}{16y}\right)$?

Accepted Answer

$\ln(7x) - \ln(16y)$

College Algebra Exam 3 Practice: Polynomial, Rational, Exponential, and Logarithmic Functions

Study Guide - Practice Questions