Graph Features of the Polynomial Function f(x) = 2x^3 + 2x^2

Math Problem Statement

Which of the following features would NOT be represented on a sketch of the graph of the function: f(x) = 2x^3 + 2x^2 - 2x + 2?

To solve this problem, we need to analyze the function:

$f(x) = 2x^3 + 2x^2 - 2x + 2$

The question asks which feature is NOT represented in the graph of the function.

Vertical Asymptote: A vertical asymptote occurs when the function tends towards infinity as $x$ approaches a specific value, usually because of a division by zero in a rational function. However, $f(x)$ is a polynomial function, and polynomial functions do not have vertical asymptotes. Therefore, option 1 (vertical asymptote at $x = 0$ ) is incorrect.
Y-Intercept: The y-intercept occurs when (

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Polynomial Functions
Graph Analysis
Vertical Asymptotes
Local Extrema

f(x) = 2x^3 + 2x^2 - 2x + 2

There are no vertical asymptotes in polynomial functions.

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