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.

$y=-3sec\left(\frac{\mathrm{\pi }}{2}x\right)$

Short answer

The graph is

Domain is $\left\{x|x\ne \pm k,kisanoddinteger\right\}$

Range is$(-\infty ,-3]\cup [3,\infty )$

Step-by-step solution

Step 1. Given information

We have been given the function as$y=-3sec\left(\frac{\mathrm{\pi }}{2}x\right)$

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 $\left\{x|x\ne \pm k,kisanoddinteger\right\}$

Range is$(-\infty ,-3]\cup [3,\infty )$