Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $24-32$, graph each function. Each graph should contain at least two periods. Use the graph to determine the domain and the range of each function.

$y=4 \sin \left(2x+4\right)-2$.

Step-by-Step Solution

Answer

The graph of the function $y=4 \sin \left(2x+4\right)-2$ is,

The domain of this function is, $\left(-\infty ,\infty \right)$.

The range of this function is, $[-4,4]$.

Step 1 Given function is,

$y=4 \sin \left(2x+4\right)-2$.

The graph of this function is,

Step 2 Find the domain and the range.

From the graph,

The domain of this function is the set of all the real numbers or $\left(-\infty ,\infty \right)$.

The range of this function is,$\left\{y|-4\le y\le 4\right\}$ or $[-4,4]$.