Answer:
Refer the attached graph below.
Step-by-step explanation:
Given : Function [tex]f(x) = 2x^6 -2x^2 -5[/tex]
To find : Which graph shows the end behavior of the graph of the given function?
Solution :
We have given the function [tex]f(x) = 2x^6 -2x^2 -5[/tex]
To find the end behavior of the graph,
We need to find the degree of the given function and the leading coefficient.
Degree of the given function is the highest power of the variable.
Highest power of x is 6.
Degree = 6 ( an even degree)
Leading coefficient is the coefficient of highest power term.
We have highest power term is [tex]2x^6[/tex].
So, the leading coefficient is 2 (Positive number)
For even degree and positive leading coefficient, end behavior is
[tex]x \rightarrow \infty, f(x) = +\infty\\\\x \rightarrow -\infty, f(x) = +\infty\\[/tex]
Refer the attached figure below.
