Question

What is period of the function, give the exact value

Answer 1

Step 1:

Find the midline

`\begin{gathered} Midline\text{ = }\frac{maximum\text{ + minimum}}{2} \\ Maximum\text{ = 11.4} \\ minimum\text{ = -5.5} \\ midline\text{ = }\frac{11.4\text{ + \lparen-5.5\rparen}}{2} \\ midline\text{ = }(5.9)/(2) \\ midline\text{ = 2.95} \end{gathered}`

Step 2:

Find the amplitude

`\begin{gathered} Amplitude\text{ = }\frac{maximum\text{ - minimum}}{2} \\ Amplitude\text{ = }\frac{11.4\text{ - \lparen-5.5\rparen}}{2} \\ Amplitude\text{ = 8.45} \end{gathered}`

Step 3:

Period:

To find the period, use the values of x.

`\begin{gathered} Period\text{ = 2\lparen11.4 + 5.5\rparen} \\ Period\text{ = 2 }*\text{ 16.9} \\ period\text{ = 33.8} \end{gathered}`

Final answer

Period = 33.8