Question

Without using technology, describe the end behavior of f(x) = -3x4 + 7X2 - 12x + 13.

Down on the left down on the right

Down on the left, up on the right

Up on the left, down on the right

Up on the left, up on the right

Answer 1

Answer: Down on the left, down on the right

Proof of validity is shown below.

Answer 2

Option 1 - Down on the left down on the right

Explanation:

Given : Function
`f(x)=-3x^(4)+7x^(2)-12x+13`

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
`f(x)=-3x^(4)+7x^(2)-12x+13`

The the end behavior of power functions of the form
`f(x)=ax^n` where n is a non-negative integer depending on the power and the constant.

The leading term,
`f(x)=-3x^(4)`

Negative constant and even power.

So, At
`x\rightarrow \infty`

`f(x)\rightarrow -\infty`

At
`x\rightarrow -\infty`

`f(x)\rightarrow -\infty`

i.e. the curve approaches down on the left and down on the right.

Therefore, option 1 is correct.