SOLUTION: The graph has an equation in the form of f(x) = a(1/2)^b(x+2)+k. What is the actual equation? Please view the graph at: https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIi

Question 1181096: The graph has an equation in the form of f(x) = a(1/2)^b(x+2)+k. What is the actual equation?
Please view the graph at:
https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

f(x) = a(1/2)^b(x+2)+k

NOTE: To make the form of the function absolutely clear, the whole exponent "b(x+2)" should be in parentheses: f(x) = a(1/2)^(b(x+2))+k

Use the two given points and the horizontal asymptote to get three equations that can be solved to determine the constants a, b, and k.

(1) horizontal asymptote:
For large values of x, the decaying exponential goes to zero, making the function close to f(x)=k. Since the asymptote is y=4, we have k=4.

(2) f(-2) = 1:

(3) f(-3) = -8:

a=-3; b=2; k=4

The function is

A graph:

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