Math  /  Algebra

QuestionThe function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=5x3+385x+80x2+490f(x)=5 x^{3}+385 x+80 x^{2}+490
Answer
as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow \infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow \infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty

Studdy Solution
Determine the end behavior based on the leading term. The leading term 5x3 5x^3 is a cubic term with a positive coefficient. The general end behavior for a cubic polynomial with a positive leading coefficient is:
- As x x \rightarrow \infty , y y \rightarrow \infty - As x x \rightarrow -\infty , y y \rightarrow -\infty
The end behavior of f(x) f(x) is: As x,y x \rightarrow \infty, y \rightarrow \infty and as x,y x \rightarrow -\infty, y \rightarrow -\infty .

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