If the minimum point on the graph of the equation y=f(x) is (-1,-3), what is the minimum point on the graph of the equation y=f(x)+5? How would I solve this problem?

Expert Answers

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`y = f(x)+5` is just the same shape as `y=f(x)` except shifted up 5 units since 5 has been added to every y value.

So if the first graph has the point (-1, -3), the second graph will have the point (-1, -3+5) or (-1, 2).

Since the two graphs have the same shape, the x value for f(x)'s minimum is the same x value for (f(x)+5)'s minimum.

Here's an example: The red graph is f(X).  The orange graph is f(x)+5. 

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