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The graph of g(x) is the result of translating the graph of f(x) = three units to the left. What is the equation of g(x)?

options

g(x)=1/2^x-3 < A

g(x)=1/2^x+3 < B

g(x)=1/2^x -3 < C

g(x)=1/2^x +3 < D

Respuesta :

scme1702
In the case of exponential functions, the graph is shifted when a constant is added to the exponent of the constant. The original equation, f(x) is:
f(x) = (1/2)ˣ
Now, when horizontal shifting is occurring, the equation is:
y = Cˣ⁺ᵃ
If a is positive, the graph shifts to the lefts and the shift is equal to a units. If a is negative, the graph shifts to the right and the shift is equal to a units. Therefore, to shift the graph 3 units to the left:

g(x) = (1/2)⁽ˣ⁺³⁾
The correct answer is B.

The equation graph of g(x) is the result of translating the graph of f(x) = three units to the left of g(x) is [tex]\rm g(x)= \dfrac{1}{2}^{x+3}[/tex].

Given

The graph of g(x) is the result of translating the graph of f(x) = three units to the left.

What is a translation of a graph?

The word translation of the graph is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Horizontal translation by h to the right (h>=0) is given by

g(x)=f(x-h)

For translation to the left, we have h=-3

g(x)=f(x-(h)) =f(x-(-3))=f(x+3)

The value of the f(x) is 1/2.

Therefore,

The equation of g(x) is;

[tex]\rm g(x)= \dfrac{1}{2}^{x+3}[/tex]

Hence, the equation of g(x) is [tex]\rm g(x)= \dfrac{1}{2}^{x+3}[/tex].

To know more about the Translation of graphs click the link given below.

https://brainly.com/question/10431107

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