What is the period of this function?
the period of the function is how long it takes for the function to start repeating.
The function starts at x = 0, we can see that it begins repeating when:
[tex]x=\frac{\pi}{2}[/tex]
Therefore, the period of the function is:
[tex]T=\frac{\pi}{2}[/tex]
What is the minimum value of this function?
From the graph we can see that the minimum value of the function is:
[tex]y_{\min }=-6[/tex]
What is the maximum value of this function?
From the graph we can see that the maximum value of the function is:
[tex]y_{\max }=-1[/tex]
What is the midline of this function?
The midline of the function is the horizontal line halfway between the function's maximum and minimum values, therefore:
[tex]ml=\frac{y_{\min }+y_{\max }}{2}=\frac{-6-1}{2}=-\frac{7}{2}=-3.5[/tex]
What is the amplitude of this function?
The amplitude of the function is the distance between the function's maximum value and the midline.
[tex]A=y_{\max }-ml=-1-(-3.5)=2.5[/tex]
Define a function, g, to represent the behavior of the graphed function.
g(a)=
This function can be described, using the following formula:
[tex]y(x)=2.5\sin (4x)-3.5[/tex]
