Which answer describes the transformation of g(x)=log4(x−2)+4 from the parent function f(x)=log4x?
It is the graph of f(x)
shifted 2 units right and 4 units up.
It is the graph of f(x)
shifted 2 units left and 4 units down.
It is the graph of f(x)
shifted 4 units left and 2 units down. <my choice
It is the graph of f(x)
shifted 4 units right and 2 units up.
four units up, 2 units right.
The correct answer is: "It is the graph of f(x) shifted 2 units right and 4 units up."
To determine the transformation of the function g(x) = log4(x - 2) + 4 from the parent function f(x) = log4x, we need to understand the effect of each component of the equation.
First, let's consider the function f(x) = log4x. The parent function f(x) = log4x represents the logarithm base 4 of x, which means it calculates the exponent to which 4 must be raised to obtain the value x. This is the basic logarithmic function without any transformations.
Now, let's examine the transformation in the given equation g(x) = log4(x - 2) + 4.
1. The logarithm function f(x) = log4x is shifted horizontally when (x - 2) replaces x inside the logarithm. This means the graph is shifted horizontally by 2 units to the right.
2. Since the graph is not multiplied or divided by a constant, there is no horizontal stretch or compression.
3. The function f(x) = log4x is shifted vertically upwards by 4 units. This means the graph is also shifted 4 units up.
Therefore, the correct answer is "It is the graph of f(x) shifted 2 units right and 4 units up."