Graphing the Secant Function with a Phase Shift and Reflection Over the X Axis

The video tutorial explains how to graph the function Y = -sec(π/2 * X + π/2) by first graphing its reciprocal function, cosine. It covers the necessary transformations, including amplitude, period, phase shift, and vertical shift. The tutorial provides step-by-step calculations for determining the period and X scale, and explains how to identify the phase shift. Finally, it demonstrates how to graph the cosine function and use it to graph the secant function, highlighting the role of asymptotes and reflections.

What is the first step in graphing the negative secant function?

• Graph the cotangent function

• Graph the reciprocal cosine function

• Graph the tangent function

• Graph the sine function

How do you calculate the period of a cosine function?

• π times the coefficient of X

• 2π times the coefficient of X

• π divided by the coefficient of X

• 2π divided by the coefficient of X

What is the phase shift of a function if the equation inside the cosine is π/2 X + π/2?

• -π

• π

• -1

• 1

What is the vertical translation of the function if D is not present in the transformation equation?

• Shift up by 1

• Shift up by π

• No vertical shift

• Shift down by 1

What is the effect of a negative 'A' in the transformation equation on the graph?

• Vertical stretch

• Horizontal stretch

• Reflection over the X-axis

• Reflection over the Y-axis

How do you identify asymptotes in the secant graph?

• At the maximum points of the cosine graph

• At the endpoints of the cosine graph

• At the minimum points of the cosine graph

• At the intercepts of the cosine graph

What shape do the secant graphs form between asymptotes?

• Circles

• Parabolas

• Ellipses

• Triangles