As $x \to \pm\infty$, $f(x) \to \infty$

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

Question 1

Given the polynomial function $f(x) = (x+4)(x-5)^2(x-2)^3$, which of the following statements about its zeros is correct?

Accepted Answer

The zero at $x = 2$ has multiplicity 3.

Question 2

For the rational function $f(x) = \dfrac{4x-2}{x^2-8x}$, which of the following describes its vertical asymptotes?

Accepted Answer

$x = 0$ and $x = 8$

Question 3

What is the end behavior of the polynomial $f(x) = 2x^4 - 8x$?

Accepted Answer

As $x 	o \pm\infty$, $f(x) 	o \infty$

Question 4

Given $f(x) = \dfrac{(x-3)(x+5)}{(x+3)(x-1)}$, which value(s) of $x$ make the denominator zero?

Accepted Answer

$x = -3$ and $x = 1$

Question 5

For the rational function $f(x) = \dfrac{x^2-25}{x^2+5x+25}$, what is the horizontal asymptote?

Accepted Answer

$y = 0$

Question 6

Which of the following is the correct expansion for $(x+5)^3$ using Pascal's Triangle?

Accepted Answer

$x^3 + 15x^2 + 75x + 125$

Question 7

Using the Binomial Theorem, what is the coefficient of $x^2$ in the expansion of $(x+2)^4$?

Accepted Answer

$24$

Question 8

If $f(x) = (x-2)^2(x+1)$, what is the degree of the polynomial?

Accepted Answer

$3$

Question 9

For the rational function $f(x) = \dfrac{x^2-9}{x^2-4}$, which of the following describes its holes?

Accepted Answer

No holes

Question 10

Given the polynomial $f(x) = x^4 + 10x^3 + 35x^2 + 50x + 25$, which form is this?

Accepted Answer

Standard form

Question 11

Which of the following is the correct binomial expansion for $(x+2)^5$?

Accepted Answer

$x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32$

Question 12

A rational function $f(x)$ has a vertical asymptote at $x = 3$ and a hole at $x = -1$. Which of the following could be its denominator?

Accepted Answer

$(x-3)(x+1)$

Question 13

Using Pascal's Triangle, what is the coefficient of $x^2$ in the expansion of $(x+3)^4$?

Accepted Answer

$54$

Question 14

For the polynomial $f(x) = (x-2)^2(x+3)$, what is the $y$-intercept?

Accepted Answer

$-12$

Question 15

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

Accepted Answer

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

Question 16

If $f(x) = \dfrac{x^2-16}{x^2-8x+16}$, what is the domain of $f(x)$?

Accepted Answer

All real numbers except $x = 4$

Question 17

Which of the following is the correct application of the Binomial Theorem for $(a+b)^n$?

Accepted Answer

$(a+b)^n = \sum_{k=0}^{n} C(n,k) a^{n-k} b^k$

Question 18

Given $f(x) = (x-1)^2(x+2)$, which statement about the graph is true?

Accepted Answer

The graph touches the $x$-axis at $x = 1$.

Question 19

If a rational function has the same degree in the numerator and denominator, what is the horizontal asymptote?

Accepted Answer

The ratio of the leading coefficients

Factored and General Forms of Polynomial and Rational Functions; Pascal's Triangle and the Binomial Theorem

Study Guide - Practice Questions