The maximum value of the function is 9/4.
The minimum value of the function is -1/4.
On the interval (0, pi/2), the function is strictly increasing.
The range of the function is [-1/4, 9/4].
Given function is:
[tex]y = \frac{5}{4} sin x +1[/tex]
What is the range of sin x?
The range of sin x is [-1, 1].
So the range of [tex]\frac{5}{4} sin x[/tex] will be [-5/4, 5/4]
So the range of [tex]\frac{5}{4} sin x +1[/tex] will be [-5/4 + 1, 5/4 +1]
The range of [tex]\frac{5}{4} sin x +1[/tex] will be [-1/4, 9/4]
The maximum value of function = upper limit of the range of [tex]\frac{5}{4} sin x +1[/tex]
So, the maximum value of the function = 9/4
The minimum value of function = lower limit of the range of [tex]\frac{5}{4} sin x +1[/tex]
So, the minimum value of the function = -1/4
As we can see in the graph, in the interval (0, π/2) the function is strictly increasing.
Therefore, The maximum value of the function is 9/4.
The minimum value of the function is -1/4.
On the interval (0, pi/2), the function is increasing.
The range of the function is [-1/4, 9/4].
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