Write a logarithmic equation f(x) = alog4(x−c) corresponding to the graph shown. (Here a and c may be positive or negative numbers.) Use f(x) = log4(x) as the parent function.

Question

Write a logarithmic equation f(x) = alog₄(x−c)

 corresponding to the graph shown. (Here a and c may be positive or negative numbers.) 

Use f(x) = log₄(x) as the parent function. 

(2, -3)

Answer 1

This solution assumes that the given point (2,-3) is meant to imply that a = 2 and c = -3.

If this is the case, than we're looking at the following transformations. Starting with the parent function f(x) = log₄(x), the function log₄(x - (-3)) = log₄(x + 3)) is the parent function, but shifted to the left by 3 units.

Next, the multiplication of a = 2 on the outside gives us 2*log₄(x + 3), there the 2 will vertically stretch the parent graph by 2 units.