Final answer:
The function g(x) = log2(x – 2) + 4 is the result of a horizontal shift 2 units to the right and a vertical shift 4 units upward from the parent function f(x) = log2 x. This transformation reflects a change in the position of the original graph without altering its shape.
Step-by-step explanation:
The transformation of the function g(x) = log2(x – 2) + 4 from the parent function f(x) = log2 x involves a horizontal shift to the right by 2 units and a vertical shift upwards by 4 units.
The term (x – 2) inside the logarithm indicates a horizontal shift, where the subtraction of 2 means that every point on the graph of the parent function will move 2 units to the right. The addition of +4 outside the logarithm indicates a vertical shift, moving the graph of the parent function up by 4 units on the y-axis.
The base-2 logarithm, log2, signifies that the growth rate is doubling, and the inverse relationship between the exponential and natural logarithm can be used to express the base number b. Therefore, for transformations involving logarithms, key characteristics such as growth rate and direction of shifts can be understood using these properties.