Answered

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.



Answer :

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

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