Question

HELP ME PLEASE!

Typical exponential function, y=a^x has an asymptote ____ and y-intercept ____ .

y=0; (0,a)
y=0; (0,1)
y=a; (0,a)
y=a; (0,1)

Answer 1

@AccessDenied

Answer 2

the intercept is 1, right ?

Answer 3

That is correct, x=0; a^0 = 1. :)

Answer 4

How do I find the asymptote ?

Answer 5

Consider what happens when you use very very large values of x in both the positive and negative directions.
a^x will explode when you go for huge numbers in positive direction.
However, negative values: a^(-x) = 1/a^(x), this part goes towards zero because for larger and larger x-values, we get 1/huge number.

Answer 6

Yes...

Answer 7

That case is for a>1, I should add. For a<1 the opposite is true, but it still goes towards y=0 in the other direction.
You could plot a few examples: y = 2^x, y = 1/2^x, etc. to get a good idea of their general form. :).

Answer 8

So the asymptote is a?

Answer 9

I don't get how does it approaches zero, if you plug in bigger numbers?

Answer 10

You know the asymptote means the value it tends towards for the extremes?

Answer 11

that I did NOT know-:( Thank you