Q: If $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

$$\displaystyle f(x)$$ \text{ is undefined at } x = 2$

Question 1

Which of the following is the correct simplification of the expression $$\displaystyle \frac{2x^2$ - 8}{4x}$$ for all $$x 
eq 0$$?

Accepted Answer

$$\displaystyle \frac{x - 2}{2}$$

Question 2

Solve the equation $$\displaystyle 3$$^{2x}$$ = 27$$ for $$x.$$

Accepted Answer

$$\displaystyle x = \frac{3}{2}$$

Question 3

A biologist models the population of a bacteria culture with the function $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the population after 4 hours? (Round to the nearest whole number.)

Accepted Answer

$$\displaystyle 500e$$^{1.2}$$ \approx 1660$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is the correct solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$\displaystyle (2, 3)$$

Question 6

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

Accepted Answer

$$\displaystyle f(g(2)) = (2 + 1)^2$ = 9$$

Question 7

Which of the following is the domain of the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$\displaystyle (-\infty, 5]$$

Question 8

A chemist needs to prepare a solution by mixing a 10% saline solution with a 30% saline solution to obtain 20 liters of a 25% saline solution. How many liters of the 30% solution should be used?

Accepted Answer

$$\displaystyle 15$$

Question 9

Which of the following is the correct simplification of $$\displaystyle \log_2$(8x)$$?

Accepted Answer

$$\displaystyle 3 + \log_2$(x)$$

Question 10

Solve for $$x$$: $$\displaystyle \frac{1}{x} + \frac{2}{x+1} = 1$$

Accepted Answer

$$\displaystyle x = 2$$

Question 11

Which of the following is the sum of the first 5 terms of the geometric sequence where $$a_1 = 3$ and r = 2$?

Accepted Answer

$$\displaystyle 93$$

Question 12

If $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

$$\displaystyle f(x)$$ 	ext{ is undefined at } x = 2$

Question 13

Which of the following is the solution to the equation $$\displaystyle \sqrt{x + 3} = x - 1$$?

Accepted Answer

$$\displaystyle x = 4$$

Question 14

A car's value depreciates according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years? (Round to the nearest dollar.)

Accepted Answer

$$\displaystyle 12250$$

Question 15

Which of the following is the correct expansion of $$\displaystyle (x + 2)^3$ using the binomial theorem?

Accepted Answer

$$\displaystyle x^3$ + 6x^2$ + 12x + 8$$

Question 16

Which of the following is the solution to the system of equations: $$\displaystyle \begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$\displaystyle x = 2, y = 3$$

Question 17

Which of the following is the correct solution to $$\displaystyle \log_{10}(x^2$ - 4) = 1$$?

Accepted Answer

$$\displaystyle x = 2, x = -2$$

Question 18

Which of the following is the correct result of performing the operation $$\displaystyle (3x^2$ - 2x + 5) + (x^2$ + 4x - 3)$$?

Accepted Answer

$$\displaystyle 4x^2$ + 2x + 2$$

Question 19

Which of the following is the correct solution to the equation $$\displaystyle 2$$^{x+1}$$ = 16$$?

Accepted Answer

$$\displaystyle x = 3$$

College Algebra Syllabus and Course Overview – Math 130 (Mt. San Antonio College)

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