Find the function

Question

Given the function f(x)=-2^x+6 and the transformations (h(x)=3f(x)) write the new function and describe graphically

Answer 1

in order to obtain h(x) we simply solve for it based on our knowns:

1. h(x) = 3 * f(x) = 3* (-2^x+6)
2. Expand and you have h(x) = 18 - 3*2^x

This function takes the form of an exponential function. Let's see what we can infer with our formula:

1. we know that for x = 0, the y intercept is 18 - 3 *2⁰ = 18 -3*1 = 15
2. we know that for y = 0, we can solve for x: 18 = 3*2^x --> 6 = 2^x --> x = log(6)/log(2)
3. we know that 2^x can never be < 0, which tells us that there is a horizontal asymptote at y = 18