Sketch g(x)=f(x-2) + 1 = 1 + e^x-2

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In summary, the equation for g(x) is g(x)=f(x-2) + 1 = 1 + e^(x-2). The purpose of the f(x-2) term in the equation is to represent a horizontal shift of the original function f(x) by 2 units to the right. The + 1 term represents a vertical shift of the graph of f(x) by 1 unit upwards. The value of g(0) can be found by substituting 0 for x in the equation, and the relationship between g(x) and f(x) is that g(x) is a transformed version of f(x) with a horizontal shift of 2 units to the right and a vertical shift of
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I'm new here and I just had a question. I can't seem to get this graphing problem. Sketch g(x)=f(x-2) + 1 = 1 + e^x-2... on a graph. Thank you very much.
 
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Start with the graph of ex. Scale by dividing by e2. Finally shift up 1.
 
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Thank you very much for your help Mathman.
 

What is the equation for g(x)?

The equation for g(x) is g(x)=f(x-2) + 1 = 1 + e^(x-2).

What is the purpose of the f(x-2) term in the equation?

The f(x-2) term represents a horizontal shift of the original function f(x) by 2 units to the right. This means that the graph of g(x) will be shifted 2 units to the right compared to the graph of f(x).

What does the + 1 term in the equation represent?

The + 1 term represents a vertical shift of the graph of f(x) by 1 unit upwards. This means that the graph of g(x) will be shifted 1 unit upwards compared to the graph of f(x).

What is the value of g(0)?

The value of g(0) can be found by substituting 0 for x in the equation. This gives us g(0) = f(0-2) + 1 = 1 + e^(-2). Depending on the original function f(x), the value of g(0) will vary.

What is the relationship between g(x) and f(x)?

The relationship between g(x) and f(x) is that g(x) is a transformed version of f(x). This transformation includes a horizontal shift of 2 units to the right and a vertical shift of 1 unit upwards. The shape of the graph of g(x) will be the same as the graph of f(x), but it will be shifted on the coordinate plane.

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