Question

question 31 points 1

if the value of \\\(|a|\\)\ is _________ in the absolute value function \\(y = a|x|\\), then the graph is farther from the \\(y\\)-axis.

\\(\bigcirc\\) greater than 1

\\(\bigcirc\\) in between 0 and 1

Explanation:

Analyze the effect of the parameter \(a\)

The parent absolute value function is \(y = |x|\).
For the transformed function \(y = a|x|\), the parameter \(a\) represents a vertical stretch or compression:

• If \(|a| > 1\), the graph is vertically stretched, making it steeper and narrower (closer to the \(y\)-axis).
• If \(0 < |a| < 1\), the graph is vertically compressed, making it wider and flatter (farther from the \(y\)-axis).

Match with the given options

The question asks for the condition where the graph is "farther from the \(y\)-axis" (wider).
This corresponds to a vertical compression, which occurs when \(|a|\) is between 0 and 1.

Answer:

• greater than 1
• in between 0 and 1 (Correct answer)