Question

Which transformation can be used to obtain the graph of \(g(x) = |8x|\) from the graph of \(f(x) = |x|\)?

A) A vertical stretch by a factor of 8.

B) A horizontal compression by a factor of 8.

C) A vertical compression by a factor of 8.

D) A reflection across the y-axis followed by a vertical stretch by a factor of 8.

Answer 1

The transformation that can be used to obtain the graph of g(x) = |8x| from the graph of f(x) = |x| is a vertical stretch by a factor of 8.

Step-by-step explanation:

The transformation that can be used to obtain the graph of g(x) = |8x| from the graph of f(x) = |x| is A) A vertical stretch by a factor of 8.

To see this, let's compare the two functions. The function g(x) is obtained by multiplying the function f(x) by 8. This multiplication stretches the graph vertically by a factor of 8, resulting in a steeper slope and an increase in the overall height of the graph.

For example, if we consider the point (1,1) on the graph of f(x), after the vertical stretch by a factor of 8, this point would move to (1,8) on the graph of g(x).