Question 1

Which of the following is the correct solution to the equation $$-5(x-4) + 2 = 11 - (x-3)$$?

Accepted Answer

$$x = 2$$

Question 2

Given the function $$f(x) = x^2$ + 3x - 1$$, what is the difference quotient $$\frac{f(x+h)-f(x)}{h}$$?

Accepted Answer

$$2x + h + 3$$

Question 3

What is the domain of the function $$f(x) = \sqrt{x-7}$$?

Accepted Answer

$$[7, \infty)$$

Question 4

A car rental company models its cost with $$C(x) = 0.10x + 50$$, where $$x is $$the number of miles driven. What does $$C(200)$$ represent?

Accepted Answer

The cost to rent the car after driving 200 miles is $70.

Question 5

Which of the following equations represents a circle with center $$(-1, 2)$$ and radius $$3$$?

Accepted Answer

$$(x+1)^2$$ + $$(y-2)^2 = 9$

Question 6

Given the quadratic function $$f(x) = 3(x-4)^2$ - 27$$, what is the vertex of the parabola?

Accepted Answer

$$(4, -27)$$

Question 7

If the population of a town follows $$P(t) = 230,000e$$^{0.04t}$$, in what year will the population double from its 2020 value?

Accepted Answer

2037

Question 8

What is the solution to the equation $$\sqrt{y+18} + 2 = y$$?

Accepted Answer

$$y = 7$$

Question 9

Which of the following is the correct inverse of the function $$f(x) = 4x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{4}$$

Question 10

What is the average rate of change of $$f(x) = x^2$ - 4 on $$the interval $$[1,3]$$?

Accepted Answer

$$4$$

Question 11

Which of the following is the correct logarithmic form of $$7^x = y$$?

Accepted Answer

$$\log_7$ y = x$$

Question 12

What is the domain of the function $$f(x) = \log_9$(3x-6)$$?

Accepted Answer

$$(2, \infty)$$

Question 13

If an investor puts $$12,500 in a 4$$% account and $$10,500 in a 2$$% account, what is the total interest earned in one year?

Accepted Answer

$$710$$

Question 14

What is the solution to the exponential equation $$4e^{2x-5} + 3 = 11$ (rounded to three decimal places)?

Accepted Answer

$$x = 2.847$$

Question 15

Which of the following is the correct simplification of $$3\log_m x + \log_m 4 - 2\log_m y$$?

Accepted Answer

$$\log_m \frac{4x^3$}{y^2$}$$

Question 16

Given the rational function $$f(x) = \frac{3-x}{x+1}$$, what is the vertical asymptote?

Accepted Answer

$$x = -1$$

Question 17

What is the solution to the logarithmic equation $$6\log_5$(4x-3) - 2 = 16$$?

Accepted Answer

$$x = 32$$

Question 18

What is the discriminant of the equation $$x^2 - 3x + 11 = 0$ and what does it indicate about the solutions?

Accepted Answer

The discriminant is $$-35$$, indicating two imaginary solutions.

Question 19

If $$f(x) = x^3$ + 4x$$, is the function even, odd, or neither?

Accepted Answer

Odd, symmetric with respect to the origin.

College Algebra Final Exam Review – Step-by-Step Study Guidance

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