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

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 ) (b) ( g(x)=f(x + 2) ) (c) ( p(x)=-f(x) )\n(d) ( h(x)=f(x + 1)-2 ) (e) ( q(x)=\frac{1}{2}f(x) ) (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 ) (b) ( g(x)=f(x + 2) ) (c) ( p(x)=-f(x) )\n(d) ( h(x)=f(x + 1)-2 ) (e) ( q(x)=\frac{1}{2}f(x) ) (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 the transformation of (Q(x)=\frac{1}{2}f(x))

For a function (y = af(x)), if (0 < a<1), it is a vertical compression. Here (a=\frac{1}{2}), so the graph of (y = f(x)) is vertically compressed by a factor of (\frac{1}{2}).

Step2: Check the key points

The original function (f(x)) has a maximum value of (y = 6) and a minimum value of (y=-6). For (Q(x)=\frac{1}{2}f(x)), the maximum value becomes (y = 3) ((6\times\frac{1}{2})) and the minimum value becomes (y=-3) ((-6\times\frac{1}{2}))

Answer:

C.