Question

If f(x) = log(x) what is (are) the transformation(s) that occurs if g(x) = 2 * log(x)

a) Vertical stretch by a factor of 2
b) Vertical compression by a factor of 2
c) Horizontal stretch by a factor of 2
d) Horizontal compression by a factor of 2

Answer 1

The transformation that occurs when g(x) = 2 * log(x) is a vertical stretch by a factor of 2.

Step-by-step explanation:

The transformation that occurs when g(x) = 2 * log(x) is a vertical stretch by a factor of 2.

To understand this, let's compare the graphs of y = log(x) and y = 2 * log(x) on a coordinate plane. When we multiply the function by 2, every point on the graph will be vertically stretched by a factor of 2. For example, if (x, y) is a point on the graph of y = log(x), the corresponding point on the graph of y = 2 * log(x) will be (x, 2y).

This vertical stretching means that the values of g(x) will be twice as large as the values of f(x) for the same input x.