7. Graphing Absolute Value Functions
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What shape do you obtain if you reflect the given graph on any horizontal line?
Example function: y=-∣x−3∣+5
We want to write an absolute value function whose graph forms a square with the given graph. To do so, we will need to draw any horizontal line. Let's arbitrarily choose the line y=3.
Note that the triangles above are congruent. Therefore, the obtained triangle is an isosceles triangle with one right angle and two angles whose measure is 45∘. If we merge these isosceles triangles, we obtain a square.
Note that there are infinitely many functions whose graphs form a square with the given graph. The function we found, y=-∣x−3∣+5, is just one of them.