To shift the graph of a function f(x) in a units in the horizontal axis, we replace x by x - a:
[tex]f(x)\rightarrow g(x)=f(x-a).[/tex]
To shift the graph of a function f(x) in b units in the vertical axis, we sum b to the function:
[tex]f(x)\rightarrow g(x)=f(x)+b.[/tex]
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We have the parent function:
[tex]y=f(x)=2^x.[/tex]
The transformed function is:
[tex]y=2^{x+4}+3.[/tex]
1) First, we shift the function f(x) a = -4 units in the horizontal axis, we get:
[tex]f(x)=2^x\rightarrow g(x)=f(x-(-4))=f(x+4)=2^{x+4}\text{.}[/tex]
2) Secondly, we shift the function g(x) b = 3 units in the vertical axis, we get:
[tex]g(x)=2^{x+4}\rightarrow h(x)=g(x)+3=2^{x+4}+3.^{}[/tex]
We see that the transformed function h(x) is obtained by shifting f(x):
0. a = -4 units in the horizontal axis, i.e. ,4 units to the left,,
,
1. b = 3 units in the vertical axis, i.e. ,3 units up,.
Answer
C. Shifted left 4 and up 3
