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 + 1)-2 )
(e) ( q(x)=\frac{1}{2}f(x) )
(f) ( g(x)=f(-x) )
(g) ( h(x)=f(2x) )
(e) choose the correct graph of ( q(x)=\frac{1}{2}f(x) ) below.

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.