Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Match each function with its correct description.

[tex]\[
\begin{array}{ll}
f(x)=(-x+1)^3(x+2)^2(x-3) & f(x)=(-2x+1)^2(x-3)^2(x+1) \\
f(x)=(x+6)(2x-3)(x-1)^2 & f(x)=(x-2)^2(-2x-1)^2(-x+1)
\end{array}
\][/tex]

A. The degree of the function is 4, and the leading coefficient is positive.

B. The degree of the function is 5, and the leading coefficient is negative.

C. The degree of the function is 6, and the leading coefficient is negative.

D. The degree of the function is 5, and the leading coefficient is positive.

Sagot :

GinnyAnswer
To answer this question, let's analyze the provided functions based on their degrees and leading coefficients. We'll match each function to its correct description:

1. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]

- Degree: 6
- Leading Coefficient: -1

2. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]

- Degree: 5
- Leading Coefficient: 4

3. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]

- Degree: 4
- Leading Coefficient: 2

4. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]

- Degree: 5
- Leading Coefficient: -4

Now, let's match these functions to the given descriptions.

1. Degree: 4, leading coefficient: positive

The function [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex] fits this description.
- Degree: 4
- Leading Coefficient: 2 (positive)

2. Degree: 5, leading coefficient: negative

The function [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: -4 (negative)

3. Degree: 6, leading coefficient: negative

The function [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex] fits this description.
- Degree: 6
- Leading Coefficient: -1 (negative)

4. Degree: 5, leading coefficient: positive

The function [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: 4 (positive)

Thus, we have the following matches:

1. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]: Degree: 4, leading coefficient: positive
2. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]: Degree: 5, leading coefficient: negative
3. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]: Degree: 6, leading coefficient: negative
4. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]: Degree: 5, leading coefficient: positive
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.