Graphing Tangent and Cotangent Assignment

Questions and Answers

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

Stretch

Vertical shift (correct)

Reflection

Horizontal shift

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

Vertical shift

Horizontal stretch (correct)

Vertical stretch

Reflection

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

4pi

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

5pi/2 + 4npi Signup and view all the answers

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

7pi/2 + 4npi Signup and view all the answers

Which function is graphed?

y = 3tan(x) + 2 Signup and view all the answers

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

Reflected across the x-axis Signup and view all the answers

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

y = -tan(x - pi/2) Signup and view all the answers

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

Start by graphing the tangent function. Compress the graph horizontally by making the period one-half pi. Reflect the graph over the x-axis. Shift the graph up 3 units. Signup and view all the answers

Study Notes

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.

Description

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.