Question

The graph of a periodic function is given below.What is the period of this function?   What is the minimum value of this function?   What is the maximum value of this function?   What is the midline of this function?y=What is the amplitude of this function?   Define a function, g, to represent the behavior of the graphed function.g(a)=

Answer 1

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:

`x=(\pi)/(2)`

Therefore, the period of the function is:

`T=(\pi)/(2)`

What is the minimum value of this function?

From the graph we can see that the minimum value of the function is:

`y_(\min )=-6`

What is the maximum value of this function?

From the graph we can see that the maximum value of the function is:

`y_(\max )=-1`

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:

`ml=(y_(\min )+y_(\max ))/(2)=(-6-1)/(2)=-(7)/(2)=-3.5`

What is the amplitude of this function?

The amplitude of the function is the distance between the function's maximum value and the midline.

`A=y_(\max )-ml=-1-(-3.5)=2.5`

Define a function, g, to represent the behavior of the graphed function.

g(a)=

This function can be described, using the following formula:

`y(x)=2.5\sin (4x)-3.5`