Thread: exponential equation transformation....

Hi,

I have the following problem that I am stuck on. I know it is probably something basic that I am missing and I would appreciate any and all help.

Thanks,
TC

Write 2 different exponential equations with different bases if there is a y intercept of 5 and an asymptote at y=3.

I have gotten this far....

y = a^x + 4

a is the base, I know that anything to the power of 0 equals 1 so this equation satisfies the y-intercept part but I am at a loss about finding some way to have an asymptote at y=3

Hello, TC!

This is trickier than you think . . .

Write two different exponential equations with different bases
which have a y-intercept of 5 and an asymptote at y=3.

An exponential function can have a coefficient in front: .

This equation has a horizontal asymptote at (the x-axis).

To have an asymptote at , we must "raise" the function 3 units.
. . So we have: .

To have a y-intercept of 5, we want: . and
. . Substitute: .

Hence, the function is: .


This equation has a graph with a y-intercept of 5 and an asymptote at .
It already satisfies the problem . . . the base does not matter.

So pick any two positive bases (other than 1).

I'd offer: .

. . but you can use your imagination . . .


Examples

. .

. .

Thank you so much! I was approaching it from the y-intercept not the asymptote.

I appreciate the assistance.

TC

we could also just change the x to a -x


so two would be:

the asymptotes and intercepts would remain the same, but you would reflect one graph in the y-axis to get the other