Question

the graph of a function ( f ) is illustrated to the right. use the graph of ( f ) as the first step toward graphing each of the following functions. (a) ( f(x)=f(x)+3 ) (b) ( g(x)=f(x + 2) ) (c) ( p(x)=-f(x) ) (d) ( h(x)=f(x + 2)-2 ) (e) ( q(x)=\frac{1}{2} f(x) ) (f) ( g(x)=f(-x) ) (g) ( h(x)=f(2x) ) (b) choose the correct graph of ( g(x)=f(x + 2) ) below.

Explanation:

Step1: Recall the horizontal shift rule

For a function \(y = f(x + h)\), if \(h>0\), the graph of \(y = f(x)\) is shifted \(h\) units to the left. Here \(G(x)=f(x + 2)\), so \(h = 2\).

Step2: Analyze the key - points

The original function \(y = f(x)\) has key - points. For example, if we consider a general point \((x_0,y_0)\) on \(y = f(x)\), then the corresponding point on \(y = f(x + 2)\) is \((x_0-2,y_0)\).

Answer:

B. Option Text