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Precalculus: An Investigation of Functions

David Lippman

Chapter 3

Polynomial and Rational Functions - all with Video Answers

Educators


Section 1

Power Functions & Polynomial Functions

01:44

Problem 1

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=x^{4}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:22

Problem 2

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=x^{6}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:13

Problem 3

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=x^{3}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:21

Problem 4

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=x^{5}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:23

Problem 5

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=-x^{2}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:07

Problem 6

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=-x^{4}
$$

Khushbu Rani
Khushbu Rani
Numerade Educator
01:22

Problem 7

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=-x^{7}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:13

Problem 8

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
f(x)=-x^{9}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:09

Problem 9

Find the degree and leading coefficient of each polynomial.
$$
4 x^{7}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:02

Problem 10

Find the degree and leading coefficient of each polynomial.
$$
5 x^{6}
$$

Melissa Barry
Melissa Barry
Numerade Educator
00:53

Problem 11

Find the degree and leading coefficient of each polynomial.
$$
5-x^{2}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:12

Problem 12

Find the degree and leading coefficient of each polynomial.
$$
6+3 x-4 x^{3}
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:03

Problem 13

Find the degree and leading coefficient of each polynomial.
$$
-2 x^{4}-3 x^{2}+x-1
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:09

Problem 14

Find the degree and leading coefficient of each polynomial.
$$
6 x^{5}-2 x^{4}+x^{2}+3
$$

Melissa Barry
Melissa Barry
Numerade Educator
02:08

Problem 15

Find the degree and leading coefficient of each polynomial.
$$
(2 x+3)(x-4)(3 x+1)
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:55

Problem 16

Find the degree and leading coefficient of each polynomial.
$$
(3 x+1)(x+1)(4 x+3)
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:33

Problem 17

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
-2 x^{4}-3 x^{2}+x-1
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:09

Problem 18

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
6 x^{5}-2 x^{4}+x^{2}+3
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:26

Problem 19

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
3 x^{2}+x-2
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:35

Problem 20

Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$.
$$
-2 x^{3}+x^{2}-x+3
$$

Melissa Barry
Melissa Barry
Numerade Educator
02:00

Problem 21

What is the maximum number of $x$ -intercepts and turning points for a polynomial of degree $5 ?$

Melissa Barry
Melissa Barry
Numerade Educator
02:23

Problem 22

What is the maximum number of $x$ -intercepts and turning points for a polynomial of degree $8 ?$

Melissa Barry
Melissa Barry
Numerade Educator
00:18

Problem 23

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:12

Problem 24

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:16

Problem 25

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:10

Problem 26

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:24

Problem 27

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:18

Problem 28

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:18

Problem 29

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
00:16

Problem 30

What is the least possible degree of the polynomial function shown in each graph?

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
02:57

Problem 31

Find the vertical and horizontal intercepts of each function.
$$
f(t)=2(t-1)(t+2)(t-3)
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:41

Problem 32

Find the vertical and horizontal intercepts of each function.
$$
f(x)=3(x+1)(x-4)(x+5)
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:26

Problem 33

Find the vertical and horizontal intercepts of each function.
$$
g(n)=-2(3 n-1)(2 n+1)
$$

Melissa Barry
Melissa Barry
Numerade Educator
01:37

Problem 34

Find the vertical and horizontal intercepts of each function.
$$
k(u)=-3(4-n)(4 n+3)
$$

Melissa Barry
Melissa Barry
Numerade Educator