Question #7db55

1 Answer
Dec 18, 2017

The graph of #g(x)=1/x+4# is the graph of #f(x)=1/x# shifted upward 4 units.

Explanation:

First, you could graph these two functions by plugging in some x values.

Graph of #1/x=f(x)#
graph{1/x [-10, 10, -5, 5]}

Graph of #1/x+4=g(x)#
graph{1/x +4[-10, 10, -5, 5]}

We see that the graph of #1/x# has been shifted upward 4 units.

There is a general rule for these "changes" in functions.
Here are the basic few:

If #f(x)=x+z#, then
#f(x)=x+z+y# makes the original function shift y units upward.
#f(x)=x+z-y# makes the original function shift y units downward.
#f(x)=(x+y)+z# makes the original function shift y units to the left.
#f(x)=(x-y)+z# makes the original function shift y units to the right.