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

Answer:

$y=3(2)^{x-5}+6$

Step-by-step 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,

$y=3(2)^{x-5}+6$