if the minimum point on the graph of the equation y=f(x) is (-1,-3). what is the minimum point on he graph of the equation y=f(x)+5 how would i go about solving this problem ...any help is greatly...

if the minimum point on the graph of the equation y=f(x) is (-1,-3). what is the minimum point on he graph of the equation y=f(x)+5 

how would i go about solving this problem ...any help is greatly appreciated!!!!

Asked on by mariaaa95

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted on

`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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