Question

Graph the following function: y = 3cot(π/4x). Determine how the general shape of the graph, chosen in the previous step, would be shifted, stretched, and reflected for the given function. Graph the result.

Answer 1

To graph the function y = 3cot(π/4x), start with the parent cotangent function and apply the given transformations.

Step-by-step explanation:

To graph the function y = 3cot(π/4x), we can start by identifying the parent function, which is the cotangent function. The general shape of the graph of the cotangent function is a series of repeating vertical stretches and compressions of the cosine curve. The graph has vertical asymptotes where the cosine function equals zero, and each period is π units long.

For the given function y = 3cot(π/4x), the graph will undergo the following transformations:

1. A vertical stretch or compression by a factor of 3.
2. A horizontal compression by a factor of π/4.
3. A reflection about the x-axis due to the negative coefficient in front of the cotangent function.

To graph the result, start with the parent cotangent function, apply the transformations, and plot the points that correspond to key values of x. Connect the points to create the graph.