Question

a) How is the graph of\({\bf{y = 2sinx}}\)related to the graph of

\({\bf{y = sinx}}\)? Use your answer and Figure 18(a) to sketch the graph of\({\bf{y = 2sinx}}\).

(b) How is the graph of \({\bf{y = 1 + }}\sqrt {\bf{x}} \)related to the graph of\({\bf{y = }}\sqrt {\bf{x}} \) ? Use your answer and Figure 17(a) to sketch the graph of\({\bf{y = 1 + }}\sqrt {\bf{x}} \).

Short answer

Graphs are given below:

Step-by-step solution

Step 1 :(a) The graph of \({\bf{y = 2sinx}}\) is given below:

The graph of\(y = 2\sin x\), we get by stretching the graph of\(y = \sin x\)vertically by a factor of 2.

(b) The graph of \({\bf{y = 1 + }}\sqrt {\bf{x}} \) is given below:

Here, the graph of\(y = 1 + \sqrt x \) can be obtained by shifting the graph\(y = \sqrt x \) by 1 unit upward.