Question

Determined if the graph represents a polynomial function if it does determine the number of turning points and the least degree

Answer 1

• The graph of f is a polynomial function
• There are two turning points, namely, x = 0  and x = -2

Explanation:

A polynomial function in one variable is given by the form:

$f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}$

Since you haven't provided any expression, I'll choose the following function:

$f(x)=x^{3}+3x^{2}+3$

So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:

$f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\ and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}$

Conclusion:

• The graph of f is a polynomial function
• There are two turning points, namely, x = 0  and x = -2

Learn more:

Polynomial function: brainly.com/question/13729121

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