Q. 107 - Precalculus Enhanced with Graphing Utilities

Question

Open the Amplitude applet. On the screen you will see a slider. Move the point along the slider to see the role a plays in the graph of $f\left(x\right)=a\sin x$. 

Step-by-Step Solution

Answer

The a in the graph $f\left(x\right)=a\sin x$ denotes the maximum and the minimum value to which the function value lies.

Step 1. Use the applet

The slider is moved and the result can be seen as

Step 2. Observation

It can be seen that as $a$ increase the maximum and the minimum value also increases.

Also, when a is multiplied to the function $y=\sin x$, to get the function $y=a\sin x$ the graph is vertically stretched by a factor of $a$.

And now the range of the function lies between the value $-a$ to $a$.