Question

Select the correct answer from each drop-down menu.The graph of the function /(=)foin(a) + I is shown. What are the key features of this function?y

Answer 1

Given:

`f(x)=(5)/(4)sin(x)+1`

Required:

We need to find the maximum, minimum, range, and interval of the increasing function.

Step-by-step explanation:

We know that the maximum value of the function occurs whenever sinx=1.

Substitue sin(x)=1 in the given equation to find the maximum value.

`The\text{ maximum}=(5)/(4)(1)+1`
`The\text{ maximum}=(5)/(4)+(4)/(4)`
`The\text{ maximum}=(9)/(4)`
`The\text{ maximum}=2.25`

We know that the minimum value of the function occurs whenever sinx=-1.

Substitue sin(x)=-1 in the given equation to find the maximum value.

`The\text{ minimum=}(5)/(4)(-1)+1`
`The\text{ minimum=}(-5)/(4)+(4)/(4)`
`The\text{ minimum=}(-1)/(4)`
`The\text{ minimum=-0.25}\frac{}{}`
`\text{ Consider the interval }(0,(\pi)/(4))`

if the value of y is increasing on increasing the value of x, then the function is known as an increasing function

The given function is increasing to the maximum value when the value of x is increasing.

The values of the given function are increasing in the given interval.

`In\text{ the interval \lparen0,}(\pi)/(4))\text{ the function is increasing.}`

We know that the range of the function lies between the minimum and maximum values.

`Range=[-0.25,2.25]`

Final answer:

`The\text{ maximum}=2.25`
`The\text{ minimum=-0.25}\frac{}{}`
`In\text{ the interval \lparen0,}(\pi)/(4))\text{ the function is increasing.}`

`Range=[-0.25,2.25]`