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The graph of y = f(x) is shown below, with one unit between grid lines. Assume f(x) is defined only on the domain shown. What is the sum of all integers c for which the equation f(x) = c has exactly 6 solutions?

 

 Oct 26, 2021
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Note that f(x) = 1 has exactly 6 solutions (draw a line through y = 1 and count how many times it cuts through the curve).

Also, f(x) = 2 has exactly 6 solutions (draw a line through y = 2 and count how many times it cuts through the curve).

Also, f(x) = ...

 

Continue in this way until the line through the integer value of y does not cut through the curve exactly 6 times.

 

Because you said there is one unit between lines, I've assumed the fine grid is numbered 1, 2 etc.  However, your labels give the coarse grid as  having labels 1, 2 etc, in which case, only the value f(x) = 1, is relevant.

 Oct 26, 2021
edited by Alan  Oct 26, 2021
edited by Alan  Oct 26, 2021

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