Question

consider the function ( f(x)=e^{x} ) and the function ( g(x) ), which is shown below. how will the graph of ( g(x) ) differ from the graph of ( f(x) )?
( g(x)=f(x)+2=e^{x}+2 )
oa. the graph of ( g(x) ) is the graph of ( f(x) ) shifted down 2 units.
ob. the graph of ( g(x) ) is the graph of ( f(x) ) shifted 2 units to the left.
oc. the graph of ( g(x) ) is the graph of ( f(x) ) shifted 2 units to the right.
od. the graph of ( g(x) ) is the graph of ( f(x) ) shifted up 2 units.

Explanation:

For a function \(y = f(x)+k\), when \(k>0\), the graph of \(y = f(x)\) is shifted up by \(k\) units. In the given functions \(f(x)=e^{x}\) and \(g(x)=e^{x}+2\), here \(k = 2>0\).

Answer:

D. The graph of \(g(x)\) is the graph of \(f(x)\) shifted up 2 units.