Long description
The dashed curve y = cosine of x oscillates about y = 0 with amplitude 1, period 2 pi, and maximum (2 pi, 1). The dashed graph y = secant of x is periodic about the x-axis with asymptotes at x = pi over 2, x = 3 pi over 2, and x = 5 pi over 2. A parabola opens upward with a vertex at (0, 1), and another opens downward with a vertex at (pi, negative 2); the vertices are at the maximums and minimums of the cosine of x curve. The solid graph y = secant of x is periodic about the x-axis with alternating upward and downward opening parabolas. A parabola opens upward with a vertex at (0, 3), another opens downward with a vertex at (pi, negative 3).
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