Question

Let the graph of h be a horizontal stretch by a factor of 3 followed by a translation 7 units right of the graph of f(x)=x. Write a rule for h. h(x)=

Answer 1

The rule for the function h after applying a horizontal stretch by a factor of 3 followed by a translation 7 units to the right to f(x) = x is h(x) = (x - 7) / 3.

Step-by-step explanation:

A student is asking how to write a rule for a new function h(x) that is derived from an existing function f(x) = x through transformations. Specifically, f(x) is to be horizontally stretched by a factor of 3 and then translated 7 units to the right.

To apply a horizontal stretch by a factor of 3 to f(x) = x, we need to divide the input variable by 3, which gives us the new function g(x) = ¼x. Then, to translate this function 7 units to the right, we subtract 7 from the input variable, resulting in the transformed function h(x). Therefore, the final rule for h(x) after applying both transformations is h(x) = (x - 7) / 3.