Question

Given , what would be the function rule for a horizontal stretching of f(x) by scale factor 4?

Answer 1

A horizontal stretch of the function f(x) by a scale factor of 4 is achieved by multiplying the input x by ¼. The new function becomes f(¼x), resulting in the points on the graph being spread out horizontally by a factor of 4.

Step-by-step explanation:

To determine the function rule for a horizontal stretching of the function f(x) by a scale factor of 4, the input variable x needs to be adjusted. In the context of transformations of functions, a horizontal stretch can be accomplished by multiplying the input variable by the reciprocal of the scale factor.

Since the scale factor given is 4, the reciprocal is ¼. Thus, the new function after the horizontal stretch will be f(\(¼\)x).

For example, if the original function is f(x) = x², a horizontal stretch by a factor of 4 would result in the function g(x) = f(\(¼\)x) = (\(¼\)x)². Simplifying g(x) gives us g(x) = \(¼\)x² = \(½\)x².

Therefore, any point on the graph of f(x) would move horizontally to a position four times further away from the y-axis.

Answer 2

Step-by-step explanation:

It appears that there's a formatting issue in your question, and the function rule is not specified. However, if you have a function
f(x) and you want to horizontally stretch it by a scale factor of 4, the rule for the stretched function g(x) would be:

g(x)=f( x/4)

In this case, you replace
x in the original function
f(x) with x/4