Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7$$?

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

Q: Which graph best matches the exponential function $$y = -0.25(4)^x$$?

Decreasing, negative, approaches zero from below as $$x \to \infty$$

Question 1

A ball is hit and its height in meters, $$h$$, as a function of the horizontal distance $$d (in $$meters) traveled, is given by $$h(d) = -0.04d^2$ + 0.74d + 1.8. $$What is the maximum height the ball reaches?

Accepted Answer

$$h_{max} = 8.6$$ meters

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 16x + 32$$, what is the vertex of the parabola?

Accepted Answer

$$(4, 0)$$

Question 3

Which of the following is the factored form of the quadratic function $$f(x) = x^2$ - 6x + 9$$?

Accepted Answer

$$(x - 3)^2$

Question 4

For the exponential growth function $$y = 100(1.08)^t$$, what is the percent rate of change per time period?

Accepted Answer

$$8\%$$

Question 5

Suppose $$1500 is $$invested in an account yielding interest at a nominal rate of $$6\%$$ per year, compounded monthly. What is the effective annual yield?

Accepted Answer

$$6.17\%$$

Question 6

Order the numbers $$e, e$$^{1/3}$$, 2^2$, 6^1$, 10^1$ from smallest to largest.

Accepted Answer

$$e^{1/3}$$, $$2^2$$, e, $$6^1$$, $$10^1$$

Question 7

An investment of $$70$$ increases in value at a continuous rate of $$4.2\%$$ per year. What is its value in $$4$$ years?

Accepted Answer

$$70e^{0.042 	imes 4}$$

Question 8

What is the value of the number $$e$$, and why is it important in mathematics?

Accepted Answer

$$e \approx 2.718$$, it is the base of natural logarithms and arises in continuous growth and decay models.

Question 9

Rewrite $$\log_{8} 0.001$$ using exponents.

Accepted Answer

$$8^x = 0.001$$

Question 10

Solve for $$x$$: $$e^{0.013x} = 100$

Accepted Answer

$$x = \frac{\ln(100)}{0.013}$$

Question 11

Convert $$Q = 10$$^{2.3t}$$ to the form Q$$ = $$ae^{kt}.$$

Accepted Answer

$$Q = e$$^{2.3t \ln(10)}$$

Question 12

Determine the half-life of a radioactive substance that decays at a continuous rate of $$7\%$$ per day.

Accepted Answer

$$t_{1/2} = \frac{\ln(2)}{0.07}$$ days

Question 13

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7$$?

Accepted Answer

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

Question 14

Given the rational function $$f(x) = \frac{2x^2$ - 3x + 1}{x^2$ - 1}$$, what are its vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 15

Which graph best matches the exponential function $$y = -0.25(4)^x$$?

Accepted Answer

Decreasing, negative, approaches zero from below as $$x 	o \infty$$

Question 16

A $$5000$$ investment earns $$6\%$$ annual interest, and a $$4000$$ investment earns $$8\%$$, both compounded continuously. When will the smaller investment catch up to the larger one?

Accepted Answer

$$t = \frac{\ln(5/4)}{0.08 - 0.06}$$ years

Question 17

Which of the following is the standard form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 18

If the graph of a quadratic function opens upward, what can you say about the leading coefficient?

Accepted Answer

It is positive.

Question 19

Given the exponential function $$f(x) = ab^x$$, which statement is true if $$0 \u003c b \u003c 1$$?

Accepted Answer

The function represents exponential decay.

Precalculus Exam 1 Review: Quadratic, Polynomial, and Exponential Functions

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