Questions: f(x)=-2x+2 f(x)=-2x^2-7x f(x)=-1/3x^4+4x^2 f(x)=x^4+2x^3 f(x)=x^2-3x f(x)=2x^3-3x+1 f(x)=-1/3x^3+x^2-4/3 f(x)=1/5x^5-2x^3+9/5x

Transcript text: (g) $f(x)=-2 x+2$ $f(x)=-2 x^{2}-7 x$ $f(x)=-\frac{1}{3} x^{4}+4 x^{2}$ $f(x)=x^{4}+2 x^{3}$ $f(x)=x^{2}-3 x$ $f(x)=2 x^{3}-3 x+1$ $f(x)=-\frac{1}{3} x^{3}+x^{2}-\frac{4}{3}$ $f(x)=\frac{1}{5} x^{5}-2 x^{3}+\frac{9}{5} x$

Solution

Solution Steps

Step 1: Identify the Degree of the Polynomial

The graph shows a polynomial function. The number of turning points suggests the degree of the polynomial. The graph has three turning points, indicating a polynomial of degree 4.

Step 2: Match the Degree with the Options

From the given options, identify which functions are of degree 4:

$ f(x) = -\frac{1}{3}x^4 + 4x^2 $
$ f(x) = x^4 + 2x^3 $

Step 3: Analyze the Leading Coefficient

The graph shows that the polynomial opens downwards on both ends, indicating a negative leading coefficient. Therefore, the correct function must have a negative leading coefficient for the highest degree term.

Final Answer

The correct function is: \[ f(x) = -\frac{1}{3}x^4 + 4x^2 \]

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