Question

A student graphed f(x)=x and g(x)=1/2f(x)-3 on the same coordinate grid. Describe how the graphs of f and g are related. (Describe the transformations)

Answer 1

5

Explanation:

Answer 2

The graph of g(x) is a transformation of f(x), involving a vertical shrink by a factor of ½ and a vertical translation downwards by 3 units.

The student has graphed two functions, f(x) = x which is a straight line with a slope of 1, and g(x) = ½f(x) - 3, on the same coordinate grid. The graph of g(x) is a transformation of the graph of f(x).

First, it is scaled down by a factor of ½, which means the slope is halved, making the graph less steep.

Then, the graph is shifted downwards by 3 units. This is indicated by the subtraction of 3 in the function, which affects the y-values.

Therefore, the two main transformations are a vertical shrink by a factor of ½ and a vertical translation downwards by 3 units.