find the vertical shift of the sinusoidal function.\nsimplify any fractions.\nvertical shift = \n

Explanation:

Step1: Identify mid - line

The mid - line of a sinusoidal function is the horizontal line that the graph oscillates about. To find it, we can take the average of the maximum and minimum values of the function. The maximum value of the function from the graph is $y = 2$ and the minimum value is $y = 1$. The formula for the mid - line (vertical shift) $d$ of a sinusoidal function $y = a\sin(bx - c)+d$ is $d=\frac{y_{max}+y_{min}}{2}$.

Step2: Calculate the vertical shift

Substitute $y_{max}=2$ and $y_{min}=1$ into the formula: $d=\frac{2 + 1}{2}=\frac{3}{2}=1.5$.

Answer:

$1.5$