Question

if the function f(x) = x² is changed so that a new function is created, g(x) = 5x², how does g(x) compare to f(x)? the graph of (x) is wider than the graph of f(x) the graph of g(x) is narrower than the graph of f(x)

Explanation:

Step1: Recall vertical stretch rules

For a quadratic function \( y = ax^2 \), if \( |a|>1 \), the graph is vertically stretched (narrower); if \( 0<|a|<1 \), it's vertically compressed (wider).

Step2: Compare \( a \)-values

Given \( f(x)=x^2 \) (so \( a = 1 \)) and \( g(x)=5x^2 \) (so \( a = 5 \)). Since \( |5|>1 \), \( g(x) \) is a vertical stretch of \( f(x) \).

Step3: Determine width comparison

A vertical stretch with \( |a|>1 \) makes the graph narrower. So \( g(x) \)’s graph is narrower than \( f(x) \)’s.

Answer:

The graph of \( g(x) \) is narrower than the graph of \( f(x) \)