Graphing the Tangent Function

The video tutorial explains how to graph the function f(x) = -2 tan(x + π/2). It covers the key aspects of graphing tangent functions, including the lack of amplitude, determining the period, phase shift, and vertical transformations. The tutorial also discusses the effect of the negative sign and the coefficient on the graph, leading to reflections and compressions. The instructor emphasizes understanding the parent graph of tangent and how transformations affect it, concluding with a demonstration of graphing the transformed function with intercepts and asymptotes.

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

• It shifts the graph up.

• It changes the period of the graph.

• It reflects the graph over the x-axis.

• It increases the amplitude.

Why does the tangent function not have an amplitude?

• Because it extends to positive and negative infinity.

• Because it has a maximum and minimum.

• Because it is a linear function.

• Because it is always positive.

How is the period of the 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) = -2tan(x + π/2)?

• π/2 to the left

• π/2 to the right

• π to the left

• π to the right

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

• 2π

• π/2

• π

• π/4

What should you do if you don't know what the parent graph of tangent looks like?

• Ignore it and proceed with transformations.

• Look it up to understand the basic shape.

• Assume it is a straight line.

• Use a calculator to plot it.

How does the coefficient of 2 affect the graph of the tangent function?

• It reflects the graph over the y-axis.

• It shifts the graph to the right.

• It compresses the graph horizontally.

• It stretches the graph vertically.

What happens to the intercept of the graph after applying the phase shift?

• It moves to -π/2.

• It moves to π/2.

• It moves to π.

• It remains at the origin.

What is the purpose of using a different x-scale when graphing?

• To increase the amplitude.

• To determine specific points on the graph.

• To change the period of the graph.

• To reflect the graph over the x-axis.

What is the final step in graphing the function f(x) = -2tan(x + π/2)?

• Determine the amplitude.

• Reflect the graph over the y-axis.

• Shift the graph vertically.

• Ensure understanding of x-scale and intercepts.