Question

What is the equation of an exponential function with base=2 that has a vertical stretch by a factor of 3, a shift to the right 5 and a shift up 6 ?

Answer 1

`y=3(2)^(x-5)+6`

Explanation:

Let the equation of the exponential function with base 2 is,

`y=a(2)^(x+c)+d`

Here, a = vertical stretch

c = Horizontal shift

d = Vertical shift

If this function has a vertical stretch by a factor of 3,

Equation will be,

`y=3(2)^(x+c)+d`

If this function has a shift of 5 to the right,

Equation of the function will be,

`y=3(2)^(x-5)+d`

If this function has a shift of 6 units upwards,

`y=3(2)^(x-5)+6`