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.\n(a) ( f(x)=f(x)+3 )\n(b) ( g(x)=f(x + 2) )\n(c) ( p(x)=-f(x) )\n(d) ( h(x)=f(x + 1)-2 )\n(e) ( q(x)=\frac{1}{2}f(x) )\n(f) ( g(x)=f(-x) )\n(g) ( h(x)=f(2x) )\n(e) choose the correct graph of ( q(x)=\frac{1}{2}f(x) ) 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.\n(a) ( f(x)=f(x)+3 )\n(b) ( g(x)=f(x + 2) )\n(c) ( p(x)=-f(x) )\n(d) ( h(x)=f(x + 1)-2 )\n(e) ( q(x)=\frac{1}{2}f(x) )\n(f) ( g(x)=f(-x) )\n(g) ( h(x)=f(2x) )\n(e) choose the correct graph of ( q(x)=\frac{1}{2}f(x) ) below.

Answer

Explanation:

Step1: Analyze vertical compression

For a function (y = af(x)), when (0 < a<1), the graph of (y = f(x)) is vertically compressed by a factor of (a). Here (a=\frac{1}{2}), so for each (x)-value, the (y)-value of (Q(x)=\frac{1}{2}f(x)) is half of the (y)-value of (f(x)).

Answer:

C.