Transformations of the Tangent Function

The video tutorial explains how to graph the function f(x) = -2 tan(x + π/2). It covers key concepts such as the lack of amplitude in tangent functions, determining the period and phase shift, and the effects of graph compression. The tutorial also demonstrates how to reflect the graph over the x-axis and adjust the x scale to identify asymptotes and intercepts. The instructor emphasizes understanding the parent graph of tangent and applying transformations to graph the function accurately.

What is the effect of the negative sign in the function f(x) = -2 tan(x + π/2)?

• It changes the period of the graph.

• It shifts the graph up.

• It reflects the graph over the x-axis.

• It increases the amplitude.

Why does the tangent function not have an amplitude?

• Because it is a linear function.

• Because it extends to positive and negative infinity.

• Because it has a maximum and minimum value.

• Because it is always positive.

How is the period of the tangent function determined?

• By multiplying π by the coefficient of x.

• By subtracting π from the coefficient of x.

• By adding π to the coefficient of x.

• By dividing π by the coefficient of x.

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

• π/2 to the right

• π to the left

• π/2 to the left

• π to the right

What is the x-scale for the function f(x) = -2 tan(x + π/2)?

• π

• π/4

• π/2

• 2π

What is the role of the vertical transformation in the function f(x) = -2 tan(x + π/2)?

• There is no vertical transformation.

• It changes the period of the graph.

• It shifts the graph up or down.

• It reflects the graph over the x-axis.

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

• At π

• At -π/2

• At π/2

• At the origin

What is the effect of the coefficient 2 in the function f(x) = -2 tan(x + π/2)?

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph to the right.

• It reflects the graph over the y-axis.

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

• It is stretched vertically by a factor of 2.

• It is shifted up by 2 units.

• It is reflected over the y-axis.

• It is reflected over the x-axis and shifted left.

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

• At -π/2

• At π

• At π/2

• At the origin