Graphing the Tangent Function with a Change of Period

The video tutorial explains the differences between tangent and cotangent graphs compared to sine and cosecant graphs. It covers the concept of period and asymptotes, emphasizing that tangent graphs do not have an amplitude and their period is π instead of 2π. The tutorial demonstrates how to calculate the new period and asymptotes when transformations are applied, such as multiplying and dividing the variable x. Finally, it shows how to graph the transformed tangent function with the new asymptotes, ensuring students understand the changes in the graph's appearance.

What is a key difference between tangent graphs and sine graphs?

• Tangent graphs are restricted in height.

• Tangent graphs have an amplitude.

• Tangent graphs go infinitely up and down.

• Tangent graphs are similar to sine graphs.

How is the period of a tangent graph determined?

• By the amplitude.

• By the formula π/B.

• By the formula 2π/B.

• By the graph's height.

What happens to the period of a tangent graph when transformations are applied?

• It becomes 2π.

• It changes according to π/B.

• It remains the same.

• It is determined by the amplitude.

What are the original asymptotes of a tangent graph?

• π/4 and 3π/4

• 0 and π

• -π/2 and π/2

• -π and π

How do transformations affect the asymptotes of a tangent graph?

• They remain unchanged.

• They disappear.

• They shift vertically.

• They change based on the transformation applied.

After applying a transformation, what are the new asymptotes if the original were -π/2 and π/2?

• -4 and 4

• -2 and 2

• -π and π

• 0 and π

If the period of a tangent graph is 4, where will the next asymptote be after 2?

• At 8

• At 3

• At 10

• At 6