Given:
The function is
[tex]f(x)=x^2[/tex]
This function is changed to f(x)+9.
To find:
The effect on the graph of the function.
Solution:
The translation is defined as
[tex]g(x)=f(x)+b[/tex] .... (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
[tex]g(x)=f(x)+9[/tex] ...(2)
From (1) and (2), we get
[tex]b=9[/tex]
So, the graph of f(x) shifts 9 units up as shown in the below graph.
