Question

use the graph of $y = f(x)$ to graph the given function.
$y = 4f(x)$

Explanation:

Step1: Vertical stretch concept

For a function \(y = af(x)\), if \(|a|> 1\), it is a vertical stretch. Here \(a = 4\).

Step2: Transform key points

• The original key points of \(y=f(x)\) are \((-4,0)\), \((0,4)\), \((4,0)\).
• For \(y = 4f(x)\), when \(x=-4\), \(y = 4f(-4)=4\times0 = 0\); when \(x = 0\), \(y=4f(0)=4\times4=16\); when \(x = 4\), \(y=4f(4)=4\times0=0\).

Answer:

Graph the points \((-4,0)\), \((0,16)\), \((4,0)\) and connect them with straight - line segments. The graph of \(y = 4f(x)\) is a vertical stretch (by a factor of 4) of the graph of \(y=f(x)\).