Question

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=cot\left(\frac{1}{4}x\right)$

Short answer

The graph is

Domain is $\left\{x|x\ne \pm 4k\mathrm{\pi },kisaninteger\right\}$

Range is$\left(-\infty ,\infty \right)$

Step-by-step solution

Step 1. Given information

We have been given the function as$y=cot\left(\frac{1}{4}x\right)$

Step 2. Draw the graph of the function.

The graph is

Step 3. Find the domain and range of the given function.

By looking at the graph,

Domain is $\left\{x|x\ne \pm 4k\mathrm{\pi },kisaninteger\right\}$

Range is$\left(-\infty ,\infty \right)$