Use limits to describe the end behavior of y= 3e^(.5x) -4

Answer 1

You can either approach this graphically or algebraically:

1) Graphically

Imagine the graph y = 3e^(.5x) - 4. You could probably see that the parent function is e^x, which is an exponential function with an upward vertical translation of 4 (so asymptote at y = 4).

Limit going to the right:

As x -> infinity, y -> ∞

Limit going to the left:

As x -> -∞, y -> -4

2) Algebraically

Limit going to the right:

lim_x->∞ 3e^(.5x) -4 = ∞

Limit going to the left:

lim_x->-∞ 3e^(.5x) -4 = 3/e^(∞) - 4

= -4

Answer 2

y = 3e^(.5x) -4

as x approaches infinity, y approaches infinity

as x approaches negative infinity, y approaches -4