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

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

Q: Given the zeros $$x = 1$$, $$x = -2$$, and $$x = 3$$ for a cubic polynomial $$f(x)$$, and $$f(0) = 12$$, what is $$f(x)$$?

$$f(x) = -2(x - 1)(x + 2)(x - 3)$$,\ \text{where the leading coefficient is found using } f(0) = 12$

Q: Solve the rational inequality $$\frac{x - 2}{x + 1} \u003e 0.$$

$$x \u003e 2 or$$ $$x \u003c -1$$,\ x \neq -1$

Question 1

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

Accepted Answer

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

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + x + 6$$, which of the following is a zero of $$f(x)$$?

Accepted Answer

$$x = 3$$

Question 3

If $$f(x) = x^4$ - 2x^3$ + x^2$, what is the multiplicity of the zero at x = 0$?

Accepted Answer

2

Question 4

A chemist models the concentration of a substance over time with $$f(x) = 2x^3$ - 5x^2$ + 3x - 1. $$According to the Intermediate Value Theorem, if $$f(1) = -1$$ and $$f(2) = 5$$, what can be concluded?

Accepted Answer

There is at least one $$c in$$ $$(1,2)$$ such that $$f(c) = 0$$

Question 5

Divide $$f(x) = 2x^3$ + 3x^2$ - x + 5 by$$ $$x - 1$$ using the Remainder Theorem. What is the remainder?

Accepted Answer

$$9$$

Question 6

Which of the following is a possible rational zero of $$f(x) = 6x^3$ - 5x^2$ + 2x - 1$$ according to the Rational Zero Theorem?

Accepted Answer

$$\frac{1}{6}$$

Question 7

Given that $$2 is a $$zero of the polynomial $$f(x) = x^3$ - 3x^2$ - 4x + 12$$, which of the following is a factor of $$f(x)$$?

Accepted Answer

$$x - 2$$

Question 8

A rational function is given by $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}. $$What are the vertical asymptotes of $$f(x)$$?

Accepted Answer

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

Question 9

Which of the following describes the horizontal asymptote of $$f(x) = \frac{2x^2$ + 5}{x^2$ - 3x + 4}$$?

Accepted Answer

$$y = 2$$

Question 10

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

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 11

Which of the following is the domain of the rational function $$f(x) = \frac{1}{x^2$ - 4x + 3}$$?

Accepted Answer

All real numbers except $$x = 1$$ and $$x = 3$$

Question 12

A medical researcher models the spread of a virus with $$f(t) = 100e$$^{0.05t}$$, where t$ is in days. What is the population after 20 days?

Accepted Answer

$$100e^{1}$$

Question 13

Which of the following best describes the graph of $$f(x) = \frac{1}{x^2$}$$ compared to $$f(x) = \frac{1}{x}$$?

Accepted Answer

$f(x) = \frac{1}{$$x^2$$}$$ is always positive and symmetric about the y-axis

Question 14

A savings account earns interest compounded quarterly at an annual rate of $$8\%. If$$ $$\2000$ is deposited, what is the amount after 5$ years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A = 2000(1 + \frac{0.08}{4}$$)^{20}$$

Question 15

Given the zeros $$x = 1$$, $$x = -2$$, and $$x = 3$$ for a cubic polynomial $$f(x)$$, and $$f(0) = 12$$, what is $$f(x)$$?

Accepted Answer

$$f(x) = -2(x - 1)(x + 2)(x - 3)$$,\ 	ext{where the leading coefficient is found using } f(0) = 12$

Question 16

Solve the rational inequality $$\frac{x - 2}{x + 1} \u003e 0.$$

Accepted Answer

$$x \u003e 2 or$$ $$x \u003c -1$$,\ x 
eq -1$

Question 17

Which of the following statements about the exponential function $$f(x) = b^x ($$where $$b \u003e 1) is $$true?

Accepted Answer

The horizontal asymptote is $$y = 0$$

Question 18

A company’s value grows according to $$V(t) = 5000e$$^{0.03t}$$, where t$ is in years. How long will it take for the value to double?

Accepted Answer

$$t = \frac{\ln 2}{0.03}$$

Question 19

If $$f(x) = x^3$ - 2x^2$ - x + 2 is $$divided by $$x - 2$$ using synthetic division, what is the remainder?

Accepted Answer

$$0$$

Polynomial, Rational, and Exponential Functions: Study Guide (Ch. 2.3–2.7, 3.1)

Guida di studio - Domande di pratica

Study guide - Flashcard