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:

$f(x)=\frac{5}{4}sin(x)+1$

Required:

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

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}=\frac{5}{4}(1)+1$$The\text{ maximum}=\frac{5}{4}+\frac{4}{4}$$The\text{ maximum}=\frac{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=}\frac{5}{4}(-1)+1$$The\text{ minimum=}\frac{-5}{4}+\frac{4}{4}$$The\text{ minimum=}\frac{-1}{4}$$The\text{ minimum=-0.25}\frac{}{}$$\text{ Consider the interval }(0,\frac{\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.

$In\text{ the interval \lparen0,}\frac{\pi}{4})\text{ the function is increasing.}$

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,}\frac{\pi}{4})\text{ the function is increasing.}$

$Range=[-0.25,2.25]$