Question

The graph of the absolute value parent function, f(x) = Ixl, is stretched

horizontally by a factor of 5 to create the graph of g(x). What function is g(x)?
A. g(x) = |1/5x|
B. g(x) = |x + 5|
C. g(x) = 5|x1
D. g(x) = |5x1

Answer 1

To solve the question, we need to consider the transformation described and determine the function that represents the stretched graph.

The absolute value parent function is
`\displaystyle\sf f(x) = |x|`. According to the question, this parent function is horizontally stretched by a factor of 5 to create the graph of
`\displaystyle\sf g(x)`.

A horizontal stretch by a factor of 5 means that the x-values on the graph are multiplied by 5. In other words, the transformation can be represented as
`\displaystyle\sf g(x) = |5x|`.

Therefore, the correct function that represents the graph of
`\displaystyle\sf g(x)`, the stretched version of
`\displaystyle\sf f(x) = |x|`, is
`\displaystyle\sf g(x) = |5x|`.

The correct answer is option D:
`\displaystyle\sf g(x) = |5x|`.