Find the behavior

Question

Find the behavior of y as x→∞ and x→-∞:

 

y=2^-x

Answer 1

y = 2^-x

 

Since x is approaching negative infinity then

x will be a negative number ... Thus

2^-x will become 2 raised to a large POSITIVE  

number.  As x gets larger this will approach

positive infinity.

 

The opposite is true as x approaches positive infinity.

y = 2^-xwill be a fraction with

1 divided by 2 to a large number. This will

approach zero as x approaches infinity.

The x axis is a horizontal asymptote.

Answer 2

This is an exponential decay, since the exponent is negative.  As x increases infinitely, y decreases.  Can you guess what happens to y as x decreases infinitely?

Answer 3

The stated function is an exponential and its horizontal asymptote is the x-axis.

A drawing of this will be EXTREMELY useful, and graphs of such basic exponential functions appear in EVERY textbook.

y approaches zero as x approaches positive infinity, and y approaches infinity as x approaches negative infinity. This is quite basic.