Question

What is the effect on the graph of the function f(x)=x^2 when f(x) is changed to f(x)+9

Answer 1

Given:

The function is

$f(x)=x^2$

This function is changed to f(x)+9.

To find:

The effect on the graph of the function.

Solution:

The translation is defined as

$g(x)=f(x)+b$                .... (1)

Where, b is vertical shift.   If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The new function is

$g(x)=f(x)+9$           ...(2)

From (1) and (2), we get

$b=9$

So, the graph of f(x) shifts 9 units up as shown in the below graph.