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

$70 \times e^{0.042 \times 4} \approx 83.22$

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

$h_{max} = 8.65$ 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

$f(x) = (x - 3)^2$

Question 4

For the exponential growth function $f(x) = 100(1.07)^x$, what is the percent rate of change?

Accepted Answer

$7\%$

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

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 7

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

Accepted Answer

$e, \sqrt{10}, 2^3, 6^2, 10^3$

Question 8

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

$70 	imes e^{0.042 	imes 4} \approx 83.22$

Question 9

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

Accepted Answer

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

Question 10

Rewrite $\log_{10} 0.001$ using exponents.

Accepted Answer

$\log_{10} 0.001 = -3$

Question 11

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

Accepted Answer

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

Question 12

Convert $Q = 10^{2.4t}$ to the form $Q = ae^{kt}$.

Accepted Answer

$Q = e^{(2.4 \ln 10)t}$

Question 13

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

Accepted Answer

$t_{1/2} = \frac{\ln 2}{0.07} \approx 9.90$ days

Question 14

Which of the following is the correct description of the graph of $y = -0.25(4)^x$?

Accepted Answer

Decreasing exponential function, reflected over the $x$-axis

Question 15

Given the rational function $f(x) = \frac{2x^2 + 1}{x^2 - 4}$, what are the vertical asymptotes?

Accepted Answer

$x = 2$ and $x = -2$

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

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

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 growth factor for an exponential function is $g = 1.25$, what is the percent rate of change?

Accepted Answer

$25\%$

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

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