Question 1

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 2

A company’s revenue function is $$R(x) = 50x$$, and its cost function is $$C(x) = 30x + 200. $$What is the profit function $$P(x)$$?

Accepted Answer

Question 3

Let $$f(x) = 2x + 3$$ and $$g(x) = x^2$. What is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 3$

Question 4

Which of the following statements is TRUE about the graph of a function and its inverse?

Accepted Answer

They are symmetric about the line $$y = x.$$

Question 5

If $$f(x) = 3x - 5$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{3}$$

Question 6

Solve the radical equation: $$\sqrt{x + 4} = 6$$

Accepted Answer

$$x = 32$$

Question 7

Which of the following is the solution to the absolute value inequality $$|2x - 3| \u003c 5$$?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 8

A population grows according to the exponential model $$P(t) = 500e$$^{0.04t}$$. What is the population after 10 years?

Accepted Answer

$$P(10) = 500e$$^{0.4}$$ \approx 746$$

Question 9

Which of the following is the logarithmic form of the equation $$2^5 = 32$?

Accepted Answer

$$\log_2$ 32 = 5$$

Question 10

Expand the logarithmic expression $$\log_3$ (xy^2$)$$ using properties of logarithms.

Accepted Answer

$$\log_3$ x + 2\log_3$ y$$

Question 11

Solve for $$x$$: $$e^{2x} = 7$

Accepted Answer

$$x = \frac{1}{2}\ln(7)$$

Question 12

If $$\log_{10} x = 3$$, what is $$x$$?

Accepted Answer

$$x = 1000$$

Question 13

A bank offers an annual interest rate of 6% compounded quarterly. If you invest $$1000, what will be the value after 2 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A = 1000(1 + \frac{0.06}{4}$$)^{8}$$ \approx 1126.83$$

Question 14

Which of the following is the correct change of base formula for $$\log_b a$$?

Accepted Answer

$$\log_b a = \frac{\log_c a}{\log_c b}$$

Question 15

A logistic growth model is given by $$P(t) = \frac{1000}{1 + 9e$$^{-0.5t}$$}. $$What is the limiting population as $$t 	o \infty$$?

Accepted Answer

$$1000$$

Question 16

Which function is one-to-one?

Accepted Answer

$$f(x) = 2x + 1$$

Question 17

Solve the quadratic inequality $$x^2 - 5x + 6$$ \u003c 0$$.

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 18

Which of the following is the condensed form of $$\log_2$ 8 + \log_2$ x$$?

Accepted Answer

$$\log_2$ (8x)$$

Question 19

A medication decays in the body according to $$M(t) = 200e$$^{-0.3t}$$. How much remains after 5 hours?

Accepted Answer

$$M(5) = 200e$$^{-1.5}$$ \approx 44.6$$

College Algebra Chapter 4 & 5

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