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:
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.