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The graph shows a polynomial function f(x) of degree 3.Which statement about f(x) is true?

The graph shows a polynomial function f(x) of degree 3.Which statement about f(x) is-example-1
User Wandy
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2 Answers

16 votes
16 votes

The statement that is true about the function in the graph is A) f(x)=(x-1)^2(x+2). Therefore , A) f(x)=(x-1)^2(x+2) is correct .

let's analyze the statement and the graph further.

The given polynomial is of degree 3, and you claim that the correct expression is f(x)=
(x - 1) ^(2) ( x+2).

To verify this, consider the factors in the expression.

If you expand,
(x - 1) ^(2) ( x+2) you get a cubic polynomial.

Now, examine the behavior of the graph near x-intercepts (points where the graph crosses the x-axis).

For a cubic polynomial, there should be two turning points where the graph changes direction.

The graph exhibits this behavior and the expression matches the given graph, then A) f(x)=(x-1)^2(x+2).

Remember to consider the end behavior of the graph as well, which should reflect the odd degree of the polynomial.

This means that the function has two factors of (x-1) and one factor of (x+2). The other answer choices do not have the correct roots.

This is because the graph has a double root at x=-1 and a single root at x=2.

Question

The graph shows a polynomial function f(x) of degree 3. Which statement about f(x) is true?

A) f(x)=(x-1)^2(x+2)

B) f(x)=(x+1)^2(x-2)

C) f(x)=(x+2)^2(x-1)

D) f(x)=(x-2)^2(x-1)

User Maurice Kroon
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2.5k points
19 votes
19 votes

Step-by-step explanation

We are given a polynomial function f(x) of degree 3

User Mark Butler
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2.9k points