Question

Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?

Answer 1

GRAPH A just passed test

Answer 2

$Given \ function : \ f(x) = 2x^6-2x^2-5$

In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.

Degree of the given function is the highest power of the variable.

We have variable x there.

Highest power of x is 6.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞