exponential functions math word problem. Asap help

Question

Can some help please thanks

an exponential function with a base of 4 has been compressed horizontally by a factor of 1/3 and reflected in the x-axis. its asymptote is the line y=3. its y intercept is (0,2). Write an equation of the function

Answer 1

-4^(x/3) + 3

 

Here's how to get it:

 

 f(x) = 4^x <--- exponential function with base 4

 

 f(x) = 4^(x/3) <-- compressed horizontally by a factor of 1/3

 

f(x) = -4^(x/3) <--- reflected about the x axis

 

f(0) = -1 , so 3 must be added to get the y intercept of 2

 

f(x) = -4^(x/3) + 3

 

as x approaches negative infinity, -4^(x/3) approaches zero.

So three is the horizontal asymptote.