Graphing Tangent and Cotangent Assignment

Transform y = cot(x) to get the graph of y = 3cot[1/5(x + 2)]. Which type of transformation is NOT performed?

Which type of transformation could cause a change in the period of a tangent or cotangent function?

What is the period of the function y = tan[1/4(x - pi/2)] + 1?

Where are the asymptotes of the function y = tan[1/4(x - pi/2)] + 1?

What are the x-intercepts of the function y = tan[1/4(x - pi/2)] + 1?

Which function is graphed?

Select all that describe how the graph of y = -2cot(x + 4) - 3 differs from that of y = cot(x).

Which of the following equations would transform the tangent graph to the parent cotangent graph?

Describe how to sketch the graph of y = -tan(2x) + 3 using the parent function.

Transformations of Cotangent and Tangent Functions

To transform y = cot(x) into y = 3cot[1/5(x + 2)], a vertical shift is not applied.
A horizontal stretch is applicable to change the period of tangent or cotangent functions.

Period and Asymptotes of Tangent Function

The function y = tan[1/4(x - pi/2)] has a period of 4π.
Asymptotes occur at x = 5π/2 + 4nπ.
X-intercepts can be found at x = 7π/2 + 4nπ.

Identifying Graphs

The function graphed as y = 3tan(x) + 2 indicates that it has undergone vertical stretching and shifting.

Differences in Cotangent Graphs

The graph of y = -2cot(x + 4) differs from y = cot(x) by:
- Reflection across the x-axis.
- A vertical shift down by 3 units.
- Vertical stretching by a factor of 2.
- A horizontal shift left by 4 units.

Transforming Tangent to Cotangent

Converting the tangent graph to the parent cotangent graph can be represented by the equation y = -tan(x - pi/2).

Sketching Tangent Graphs

To graph y = -tan(2x) + 3, start with the parent tangent function and apply the following transformations:
- Compress the graph horizontally to a period of π/2.
- Reflect the graph over the x-axis.
- Shift the graph upward by 3 units.

This quiz focuses on understanding the transformations of the tangent and cotangent functions. You will analyze various transformations including vertical shifts and horizontal stretches, and determine the period of the tangent function. Enhance your skills in graphing these trigonometric functions with targeted questions.