Question

Given f(x) = |x|, what would be the function rule for a horizontal compression of f(x) by scale factor 1/8?

Answer 1

To compress the function f(x) = |x| horizontally by a scale factor of 1/8, the new function would be g(x) = |8x|. This makes the graph of the function narrower, moving the x-values closer together by a factor of eight.

Step-by-step explanation:

To perform a horizontal compression of the function f(x) = |x| by a scale factor of 1/8, we modify the argument inside the absolute value function. This involves multiplying the argument by the reciprocal of the scale factor.

The rule for the horizontally compressed function, g(x), would be:

g(x) = |8x|

A horizontal compression means that the 'x' values are scaled so that they are closer together by a factor of eight. The absolute value function normally has a 'V' shape, with the point of the 'V' at the origin. After the compression, each point on the graph of f(x) will be 1/8 the distance from the y-axis that it was originally. This results in a graph that is narrower, or 'compressed', compared to the original graph of f(x).

For example, if x were originally at 8 units from the y-axis, after applying the scaling factor of 1/8, the same x would now be at 1 unit from the y-axis.

Answer 2

Step-by-step explanation:

For a horizontal compression of

f(x)=∣x∣ by a scale factor of 1/8
, the rule for the compressed function

g(x) would be:

g(x)=∣8x∣

In this case, you multiply the variable
x inside the absolute value function by the reciprocal of the compression factor, which is 8 in this instance.