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

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

Part 1

the maximum value of the function is 2.25

For x=pi/2

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

Part 2

The minimum value of the function is -0.25

For x=-pi/2

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

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]