Respuesta :
Answer:
Option 1 - Down on the left down on the right
Step-by-step explanation:
Given : Function [tex]f(x)=-3x^{4}+7x^{2}-12x+13[/tex]
To find : Without using technology, describe the end behavior of f(x) ?
Solution :
Without technology we apply characteristics of Power and Polynomial Functions
As in function [tex]f(x)=-3x^{4}+7x^{2}-12x+13[/tex]
The the end behavior of power functions of the form [tex]f(x)=ax^n[/tex] where n is a non-negative integer depending on the power and the constant.
The leading term,[tex]f(x)=-3x^{4}[/tex]
Negative constant and even power.
So, At [tex]x\rightarrow \infty[/tex]
[tex]f(x)\rightarrow -\infty[/tex]
At [tex]x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -\infty[/tex]
i.e. the curve approaches down on the left and down on the right.
Therefore, option 1 is correct.
