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Home > PC > Chapter 7 > Lesson 7.3.3 > Problem 7-127


The graph of a transformation of has the -axis as a line of symmetry and as a point of symmetry. The line is tangent to the graph at many places. Find a possible equation.

Since is a point of symmetry, it is a point of rotational symmetry and must be on the midline.
Since the -axis is a line of symmetry, the point must also lie on the curve.

Since is on the midline, the line must be a lower boundary line.
Use this information to determine the amplitude and make a possible sketch.

Periodic curve with 3 visible turning points, at (negative 40, comma 15), (0, comma 85), & 40, comma 15), dashed horizontal lines at y = 15, y = 50, & y = 85, highlighted points on curve & center line at (negative 20, comma 50), & (20, comma 50).