Explanation:
Midline: it is a horizontal line where half of the function above it and half of the function is below it.
Amplitude: It means how far the function varies from the midline to the above and below.
Period: the distance between two consecutive maximum points (minimum points).
3) From the graph,
[tex]\begin{gathered} \text{Midline}=\frac{Maximum\text{ point+ minimum point}}{2} \\ =\frac{3+(-1)}{2} \\ =\frac{3-1}{2} \\ =\frac{2}{2} \\ =1 \end{gathered}[/tex]
Answer: Midline=1
1) Amplitude
[tex]\text{Amplitude =}2[/tex]
2) Periods
[tex]\begin{gathered} \text{Period}=6 \\ \Rightarrow b=\frac{2\pi}{6} \end{gathered}[/tex]
4) The trigonometric equation is,
[tex]\begin{gathered} y=a\cos (b(x-c))+d \\ a=\text{ amplitude} \\ b=\text{period} \\ c=\text{ phase shift} \\ d=\text{ vertical shift} \\ y=2\cos (\frac{2\pi}{6}x)+1 \end{gathered}[/tex]
Answer:
[tex]y=2\cos (\frac{2\pi}{6}x)+1[/tex]
