SOLUTION: Explain how to get the graph of the function f(x)=e^(x-2)+3 from the graph of the function g(x)=e^x.

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Question 194487: Explain how to get the graph of the function f(x)=e^(x-2)+3 from the graph of the function g(x)=e^x.
Answer by jim_thompson5910(14938) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the graph of g%28x%29=e%5Ex


+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cexp%28x%29%29%0D%0A%0D%0A%29


Now shift the graph over 2 units to the right to graph y=e%5E%28x-2%29


+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cexp%28x%29%2Cexp%28x-2%29%29%0D%0A%0D%0A%29

Graph of g%28x%29=e%5Ex (red) and y=e%5E%28x-2%29 (green)




Finally, shift the previous graph up 3 units to get the graph of f%28x%29=e%5E%28x-2%29%2B3


+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cexp%28x%29%2Cexp%28x-2%29%2Cexp%28x-2%29%2B3%29%0D%0A%0D%0A%29

Graph of g%28x%29=e%5Ex (red), y=e%5E%28x-2%29 (green), and f%28x%29=e%5E%28x-2%29%2B3 (blue)


So the graph of f%28x%29=e%5E%28x-2%29%2B3 is



+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cexp%28x-2%29%2B3%29%0D%0A%0D%0A%29