the graph of a function ( f ) is illustrated to the right. use the graph of ( f ) as the first step toward…

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.

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.

Answer

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