Given a function f(x), we know that the graph of:
• f(x - a) is the graph f(x) shifted horizontally ,a, units to the right,
,• f(x) + b is the graph f(x) shifted vertically ,b, units up,
,• f(x - a) + b is the graph f(x) shifted horizontally ,a, units to the right and vertically ,b, units up,.
Comparing the function:
[tex]y=f(x-2)+4[/tex]with the general case f(x - a) + b, we see that we have:
• a = 2,
,• b = 4.
So we conclude that the graph of this function is the graph of f(x) sifted:
• horizontally a = 2 units to the right,
,• vertically b = 4 units up.
Answer
The graph of this function is the graph of f(x) sifted:
• horizontally 2 units to the right,
,• vertically 4 units up.