Question

A student graphed f(x) = x and g(x) = 0.5f(x) on the same coordinate grid. Which statement describes the transformation of function f and function g?

A) Function g is a reflection of function f over the x-axis.
B) Function g is a horizontal compression of function f.
C) Function g is a vertical stretch of function f.
D) Function g is a translation of function f to the right.

Answer 1

The graph of g(x) = 0.5f(x) is a horizontal compression of the graph of f(x) by a factor of 0.5. Therefore, the correct statement describing the transformation of function f and function g is B) Function g is a horizontal compression of function f.

Step-by-step explanation:

When graphing f(x) = x, the resulting graph is a straight line with a slope of 1, passing through the origin (0,0). In other words, as x increases by 1, the corresponding y value also increases by 1. When graphing g(x) = 0.5f(x), the resulting graph is a horizontal compression of f(x) by a factor of 0.5. This means that the points on the graph of g(x) are half as far from the y-axis as the corresponding points on the graph of f(x). Therefore, the correct statement describing the transformation of function f and function g is B) Function g is a horizontal compression of function f.