Q: Which of the following describes the end behavior of the function $$f(x) = -2x^4$ + 3x^2$ - 5$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Q: A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 50e$$^{-0.2t}$$. What is the concentration after 5 hours?

$$50e^{-0.2 \times 5}$$ = $$50e^{-1}$$

Question 1

Which of the following statements about the roots of a polynomial function is correct?

Accepted Answer

A polynomial of degree $$n$$ has at most $$n$$ real roots, but may have fewer depending on the function.

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, which of the following is a possible rational root according to the Rational Root Theorem?

Accepted Answer

$$2$$

Question 3

Which of the following describes the end behavior of the function $$f(x) = -2x^4$ + 3x^2$ - 5$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 4

A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 50e$$^{-0.2t}$$. What is the concentration after 5 hours?

Accepted Answer

$$50e^{-0.2 	imes 5}$$ = $$50e^{-1}$$

Question 5

Which property of logarithms allows you to rewrite $$\log_b(xy) as$$ $$\log_b(x) + \log_b(y)$$?

Accepted Answer

Product property

Question 6

Solve for $$x$$: $$2^{x} = 32$

Accepted Answer

$$x = 5$$

Question 7

Which of the following is the inverse function of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{3}$$

Question 8

A population of bacteria grows according to $$P(t) = 1000e$$^{0.05t}$$. How long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln(2)}{0.05}$$

Question 9

Which of the following is NOT a property of exponential functions?

Accepted Answer

The range is all real numbers.

Question 10

If $$f(x) = x^2$ - 6x + 9$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 0)$$

Question 11

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 12

A radioactive substance decays according to $$N(t) = N_0e$$^{-kt}$$. If the half-life is 10 years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln(2)}{10}$$

Question 13

Which of the following is a correct application of the change of base formula for logarithms?

Accepted Answer

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

Question 14

If $$f(x) = x^3$ - 2x^2$ + x - 5$$, what is the degree of the polynomial?

Accepted Answer

$$3$$

Question 15

Which of the following is the correct solution to $$e^{2x} = 7$?

Accepted Answer

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

Question 16

Which of the following statements about the graph of $$f(x) = a^x$$ for $$a \u003e 1 is $$true?

Accepted Answer

The graph increases as $$x$$ increases.

Question 17

If $$f(x) = \log_3$(x)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e 0$$

Question 18

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

Accepted Answer

Question 19

A car depreciates in value according to $$V(t) = 20000e$$^{-0.15t}$$, where t$ is in years. What is the value after 3 years?

Accepted Answer

$$20000e^{-0.45}$$

Algebraic, Polynomial, Exponential, and Logarithmic Functions: Precalculus Review Notes

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