Chapter 5, Problem 38RE

To determine

Tofind:the function with the help of graph given below.

Answer to Problem 38RE

The function is $\text{y=2Sin}\frac{\text{π}}{\text{2}}x$ .

Explanation of Solution

Given:

  

Concept used:

Where $\text{A}$ is amplitude can be also deduce from the formula:

Its distance between the maximum point to the center line.

  $\text{Maxpoint-0}$ and amplitude is always taken positive.

Period is measured as distance it takes for the entire graph to repeat.

  $\text{period=}\frac{\text{2π}}{\text{B}}$ .

  $\text{B=}\frac{\text{2π}}{\text{period}}$ .

Phase shift = $\text{C}$

  $\left(\text{Positive}\text{is}\text{to}\text{the}\text{left}\right)$ .

Vertical shift= $\text{D}$ .

  $\text{y=ASin}\left(\text{B}\left(\text{x+C}\right)\right)\text{+D}$ .

Calculation:

Here the graph is $\text{Sine}$ graph since the graph is started from origin.

From the given graph:

  

The maximum point is $\text{2}$ and center line point is 0.

So, the Amplitude $\text{A=2-0=2}\text{.}$

Amplitude= $2$ .

Here maximum point cut $\frac{\text{1}}{\text{4}}\text{th}\text{of cycle}$ so, the x-axis of the maximum point is $\text{1}$ .

When it multiplies by 4 the whole cycle or period is formed.

Therefore, Period here is $\text{4}$ since the cycle started to repeat after $\text{4}$ .

Period= $\text{4}$ .

So, $\text{B=}\frac{\text{2π}}{\text{4}}\text{=}\frac{\text{π}}{\text{2}}$ .

  $\text{B=}\frac{\text{π}}{\text{2}}$ .

  $\text{C=0}$ since the graph is not shifted from origin.

  $\text{y=ASin}\left(\text{B}\left(\text{x+C}\right)\right)\text{+D}$

  $\text{y=2Sin}\left(\frac{\text{π}}{\text{2}}\left(\text{x+0}\right)\right)\text{+0}$

  $\text{y=2Sin}\frac{\text{π}}{\text{2}}x$ .

Hence the function is $\text{y=2Sin}\frac{\text{π}}{\text{2}}x$ .