Question

I don’t know how to shift equations even when it’s on a grap could you please help

Answer 1

To shift the graph of a function f(x) in a units in the horizontal axis, we replace x by x - a:

`f(x)\rightarrow g(x)=f(x-a).`

To shift the graph of a function f(x) in b units in the vertical axis, we sum b to the function:

`f(x)\rightarrow g(x)=f(x)+b.`

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We have the parent function:

`y=f(x)=2^x.`

The transformed function is:

`y=2^(x+4)+3.`

1) First, we shift the function f(x) a = -4 units in the horizontal axis, we get:

`f(x)=2^x\rightarrow g(x)=f(x-(-4))=f(x+4)=2^(x+4)\text{.}`

2) Secondly, we shift the function g(x) b = 3 units in the vertical axis, we get:

`g(x)=2^(x+4)\rightarrow h(x)=g(x)+3=2^(x+4)+3.^{}`

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