Graph the Tangent Equation with a Reflection and Phase Shift

The video tutorial explains how to graph the function F(x) = -2 tan(x + π/2). It covers key concepts such as reflection over the X-axis, the absence of amplitude for tangent functions, and the determination of period, X scale, phase shift, and vertical transformation. The tutorial emphasizes understanding the parent graph of tangent and how transformations affect it, including reflections and compressions. The instructor provides a step-by-step guide to graphing the function, focusing on identifying asymptotes and intercepts.

What is the effect of a negative sign in front of the tangent function?

• It shifts the graph upwards.

• It reflects the graph over the x-axis.

• It compresses the graph horizontally.

• It stretches the graph vertically.

Why do tangent functions not have an amplitude?

• Because they are always positive.

• Because they extend indefinitely.

• Because they are periodic.

• Because they have a maximum and minimum value.

How is the period of a tangent function determined?

• By dividing π by the coefficient of x.

• By multiplying π by the coefficient of x.

• By adding π to the coefficient of x.

• By subtracting π from the coefficient of x.

What is the phase shift of the function F(x) = -2 tan(x + π/2)?

• π/2 to the left

• π to the left

• π/2 to the right

• π to the right

What does the coefficient '2' do to the tangent graph?

• It compresses the graph horizontally.

• It reflects the graph over the y-axis.

• It stretches the graph vertically.

• It shifts the graph upwards.

Where does the graph of F(x) = -2 tan(x + π/2) start after the phase shift?

• At the origin

• At π

• At π/2

• At -π/2

How does the graph of F(x) = -2 tan(x + π/2) differ from the parent graph of tangent?

• It is shifted upwards.

• It is shifted to the right.

• It is reflected over the x-axis and compressed.

• It is stretched vertically.