Question

use the graph of ( y = f(x) ) to graph the function ( g(x)=f(x + 3) ).
choose the correct graph of ( g ) below

Explanation:

Step1: Function transformation rule

For a function \(y = f(x)\), the graph of \(y=f(x + h)\) is a horizontal shift. If \(h>0\), the graph shifts to the left by \(h\) units; if \(h < 0\), the graph shifts to the right by \(|h|\) units. Here \(g(x)=f(x + 3)\), so \(h = 3>0\), and the graph of \(y = f(x)\) shifts to the left by 3 units.

Step2: Analyze each option

• Option A: Incorrect shift direction or amount.
• Option B: Incorrect shift direction or amount.
• Option C: Correctly shifts the graph of \(y = f(x)\) to the left by 3 units.
• Option D: Incorrect shift direction or amount.

Answer:

C.