Question

Options for the first box:2.25, 1, 2 piOptions for the second box: -1, pi/2, -0.25Options for the third box: increasing and decreasingOptions for the fourth box: all real numbers, [-1,1], [-0.25, 2.25]

Answer 1

we have the function

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

Part 1

the maximum value of the function is 2.25

For x=pi/2

`\begin{gathered} f((\pi)/(2))=(5)/(4)\sin (\pi)/(2)+1 \\ f((\pi)/(2))=(5)/(4)+1 \\ f((\pi)/(2))=2.25 \end{gathered}`

Part 2

The minimum value of the function is -0.25

For x=-pi/2

`\begin{gathered} f(-(\pi)/(2))=(5)/(4)\sin (-\pi)/(2)+1 \\ f(-(\pi)/(2))=-(5)/(4)+1 \\ f(-(\pi)/(2))=-0.25 \end{gathered}`

Part 3

over the interval [0,pi/2] the function is increasing

Part 4

the range of the function is the interval [-0.25, 2.25]