Answer
The domain and range for the function $y=f\left( x \right)$ are $\left[ 0,2 \right)$ and $\left[ 0,2 \right]$respectively.
Work Step by Step
Observe the graph of the function,$y=f\left( x \right)$
According to the definition of the domain, it is the set of all the input values -- that is, the values taken for the variable x for the function $y=f\left( x \right)$.
These values are plotted on the x-axis.
According to the definition of range, it is the set of all the output values -- that is, the values obtained for the variable y for the function$y=f\left( x \right)$.
These values are plotted on the y-axis.
A black dot on the graph means that the particular point is included whereas a white dot means that the particular point is not included.
The function $y=f\left( x \right)$ takes the value from 0 to 2 but 2 is not included.
Therefore, the domain of the function is $\left[ 0,2 \right)$.
The function $y=f\left( x \right)$ gives the value from 0 to 2 and 2 is not included.
Therefore, the range of the function is $\left[ 0,2 \right]$.
Thus, the domain and range for the function $y=f\left( x \right)$ are $\left[ 0,2 \right)$ and $\left[ 0,2 \right]$ respectively.
