What is the end behavior?

Question

x(x-3)2

Answer 1

Is this supposed to be:

 

x(x-3)²  ??

 

If so then we have:

 

x(x²-6x+9) = x³-6x²+9x

 

To determine the end behavior look at the

term with the highest exponent...  In this case

that term is x³

 

As x approaches negative infinity, x³ will approach negative

infinity so to the left the end goes down.

 

As x approaches positive ∞, x³ approaches positive ∞ so to

the right the end goes up.

Answer 2

I'm reading x(x-3)2

 

Rewrite 2x² - 6x

 

Since it's a positive, even function

 

As x approaches negative infinity, y approaches positive infinity.

 

Likewise, as x approaches positive infinity, y approaches positive infinity.