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)+2 )
(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) )
(a) choose the correct graph of ( f(x)=f(x)+2 ) below.

Explanation:

Step1: Vertical shift rule

For a function \(y = f(x)+k\), if \(k>0\), the graph of \(y = f(x)\) is shifted vertically upwards by \(k\) units. Here \(k = 2\).
The original function \(y=f(x)\) has a maximum value of \(y = 8\) and a minimum value of \(y=-8\).
For \(F(x)=f(x)+2\), the new maximum value is \(y=8 + 2=10\) and the new minimum value is \(y=-8+2=-6\)

Answer:

A.