Question 1

Based on the graph provided (first image), is the function shown one-to-one?

Accepted Answer

No, because some y-values correspond to more than one x-value.

Question 2

Determine whether the function $$f(x) = 5x^3$ + 1 is $$one-to-one.

Accepted Answer

Yes, because it is a cubic function with a nonzero leading coefficient.

Question 3

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$ + 4$$

Question 4

Given $$f(x) = x^3$ - 2$$ and $$g(x) = \sqrt[3]{x+2}$$, are $$f$$ and $$g$$ inverses?

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x.$$

Question 5

Find the inverse of $$f(x) = -8x + 1.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x-1}{-8}$$

Question 6

Let $$f(x) = 5^x. $$Find $$f(2). $$Round your answer to the nearest thousandth.

Accepted Answer

$$25.000$$

Question 7

Solve for $$x$$: $$5^{-x}$$ = \frac{1}{125}$$.

Accepted Answer

$$x = -3$$

Question 8

A sum of $$\5276$ is invested for 8 years at 6% compounded annually. What is the future value? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A = 5276(1 + 0.06)^8$

Question 9

The growth in the mouse population at a county dump is modeled by $$A(t) = 383e$$^{0.019t}$$. To the nearest tenth of a month, when will the population be 616?

Accepted Answer

$$t = \frac{\ln(616/383)}{0.019}$$

Question 10

Evaluate $$\log_3$ \frac{1}{3}.$$

Accepted Answer

$$-1$$

Question 11

Write $$4^{-3}$$ = \frac{1}{64}$$ in logarithmic form.

Accepted Answer

$$\log_4$ \frac{1}{64} = -3$$

Question 12

Solve for $$x$$: $$\log_5$ x = 2.$$

Accepted Answer

$$x = 25$$

Question 13

Rewrite $$\log_a(9x^4$y)$$ using properties of logarithms.

Accepted Answer

$$2\log_a 3 + 4\log_a x + \log_a y$$

Question 14

Write the expression as a single logarithm: $$\log_3$ 12 - \log_3$ x.$$

Accepted Answer

$$\log_3$ \left(\frac{12}{x}\right)$$

Question 15

Solve for $$x$$: $$\log_2$ \frac{1}{32} = x.$$

Accepted Answer

$$x = -5$$

Question 16

Which of the following is the correct exponential form of $$\log_{16} 2 = \frac{1}{4}$$?

Accepted Answer

$$16^{1/4} = 2$

Question 17

Use properties of logarithms to simplify $$\log_3$ \frac{x^3$ y^4$}{4}.$$

Accepted Answer

$$3\log_3$ x + 4\log_3$ y - \log_3$ 4$$

Question 18

A radioactive isotope decays according to $$A(t) = 576e$$^{-0.029t}$$. To the nearest year, when will there be 139 mg left?

Accepted Answer

$$t = \frac{\ln(139/576)}{-0.029}$$

Question 19

Write $$\log_2$ 16 = 4 in $$exponential form.

Accepted Answer

$$2^4 = 16$

College Algebra: One-to-One Functions and Inverses (Graphical Analysis)

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