Questions: Which function describes the graph? f(x)=2x^3+3 f(x)=3x^2+2 f(x)=-2x^2+3 f(x)=-3x^3+2

Which function describes the graph? f(x)=2x^3+3 f(x)=3x^2+2 f(x)=-2x^2+3 f(x)=-3x^3+2
Transcript text: Which function describes the graph? $f(x)=2 x^{3}+3$ $f(x)=3 x^{2}+2$ $f(x)=-2 x^{2}+3$ $f(x)=-3 x^{3}+2$
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Solution

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Solution Steps

Step 1: Analyze the graph's behavior

The graph passes through the point (0, 2). It also has a general shape that decreases as x increases, suggesting a negative leading coefficient and an even or odd degree.

Step 2: Evaluate options at x=0

Let's evaluate each function at $x=0$ to see which one passes through the point $(0, 2)$.

  1. $f(0) = 2(0)^3 + 3 = 3$
  2. $f(0) = 3(0)^2 + 2 = 2$
  3. $f(0) = -2(0)^2 + 3 = 3$
  4. $f(0) = -3(0)^3 + 2 = 2$

Options 2 and 4 pass through (0,2).

Step 3: Analyze the shape of the graph

The graph appears to have an inflection point around $x=0$. This behavior is typical of a cubic function, not a quadratic. Option 2 is quadratic, while option 4 is cubic.

Final Answer

\\(\boxed{f(x)=-3 x^{3}+2}\\)

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