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 $$x + 2 \u003e 0$$

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

$$x \u003e 1 or$$ $$x \u003c -1$$

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

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