Question
Brandy is asked to sketch a graph of m(x)=(2x+5)(x−3)3(8x+1)5 . How many turning points should her sketch include?(1 point)
Answers
GPT-4o mini
To determine the number of turning points of the function \( m(x) = (2x + 5)(x - 3)^3(8x + 1)^5 \), we need to analyze the polynomial.
The function \( m(x) \) is a polynomial, and the number of turning points of a polynomial of degree \( n \) can be at most \( n - 1 \).
First, we need to find the degree of \( m(x) \):
- The term \( (2x + 5) \) has degree 1.
- The term \( (x - 3)^3 \) has degree 3.
- The term \( (8x + 1)^5 \) has degree 5.
Now, we add the degrees of the individual terms:
\[
\text{Degree of } m(x) = 1 + 3 + 5 = 9.
\]
Since a polynomial of degree 9 can have at most \( 9 - 1 = 8 \) turning points, Brandy should include **8 turning points** in her sketch.
The function \( m(x) \) is a polynomial, and the number of turning points of a polynomial of degree \( n \) can be at most \( n - 1 \).
First, we need to find the degree of \( m(x) \):
- The term \( (2x + 5) \) has degree 1.
- The term \( (x - 3)^3 \) has degree 3.
- The term \( (8x + 1)^5 \) has degree 5.
Now, we add the degrees of the individual terms:
\[
\text{Degree of } m(x) = 1 + 3 + 5 = 9.
\]
Since a polynomial of degree 9 can have at most \( 9 - 1 = 8 \) turning points, Brandy should include **8 turning points** in her sketch.