Question 1

Which of the following is the correct equation of the line passing through the points $$(-1, 3)$$ and $$(2, 1) in $$slope-intercept form?

Accepted Answer

$$y = -\frac{2}{3}x + \frac{7}{3}$$

Question 2

Solve the equation $$2(x+2) - 3x = 12. $$What is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 3

Given the function $$g(x) = (x+2)^2$ - 1$$, what is the vertex of the graph?

Accepted Answer

$$(-2, -1)$$

Question 4

Which of the following describes the domain of $$g(x) = (x+2)^2$ - 1$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 5

Rewrite $$f(x) = 4x^2$ - 8x - 32 in $$vertex form.

Accepted Answer

$$f(x) = 4(x-1)^2$ - 36$$

Question 6

Solve the quadratic equation $$2x^2 - 2x + 5 = 0$. What are the solutions?

Accepted Answer

$$x = \frac{1 \pm \sqrt{-9}}{2}$$

Question 7

Factor $$x^2 + 4x + 4$ completely.

Accepted Answer

$$(x+2)(x+2)$$

Question 8

Find all zeros of $$f(x) = x^3$ + 2x^2$ - 24x$$ given that $$x = 4 is a $$zero.

Accepted Answer

$$x = 0, x = -6, x = 4$$

Question 9

Solve the exponential equation $$4^{2x+5} = 16$. What is the value of x$?

Accepted Answer

$$x = -1.5$$

Question 10

Expand $$\log_4$(3x^2y^3$)$$ using properties of logarithms.

Accepted Answer

$$\log_4$ 3 + 2\log_4$ x + 3\log_4$ y$$

Question 11

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

Accepted Answer

$$2x + 1$$

Question 12

Find all asymptotes and domain of $$f(x) = \frac{4x^2$+2}{x^2$-25}.$$

Accepted Answer

Vertical asymptotes at $$x = 5$$ and $$x = -5$$, domain $$x 
eq 5, x 
eq -5$$

Question 13

Determine if $$f(x) = 2x + 12 is $$one-to-one. If so, what is its inverse?

Accepted Answer

Yes, inverse is $$f^{-1}(x$$) = \frac{x-12}{2}$$

Question 14

Which of the following graphs represents a relation that is NOT a function?

Accepted Answer

A circle centered at the origin

Question 15

Which of the following graphs represents a function that is NOT one-to-one?

Accepted Answer

A parabola opening upwards

Question 16

Which of the following graphs is NOT continuous over its entire domain?

Accepted Answer

A graph with a jump discontinuity

Question 17

Solve $$x^2 + 3x = 10$. What are the solutions?

Accepted Answer

$$x = -5, x = 2$$

Question 18

Which of the following is the correct expansion for $$\log_4$(3x^2y^3$)$$?

Accepted Answer

$$\log_4$ 3 + 2\log_4$ x + 3\log_4$ y$$

Question 19

Find the domain of $$f(x) = \frac{x-2}{x^2$+4x-5}.$$

Accepted Answer

$$x 
eq 1, x 
eq -5$$

College Algebra Final Exam Study Guide: Step-by-Step Guidance

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