Sketch y = x + 3, and then erase everything before x = -5 and after x = 2. Make sure to draw a filled-in circle for the left-hand endpoint and an "open" circle for the right-hand endpoint.
Then sketch y = x^2, and erase everything before x = 2 and after x = 4. Make sure to draw filled-in circles for each of the endpoints.
The domain is given: it's the x-values for which the function is defined.
To find the range, look at your graph. Which y-values are covered by this graph? (If you "collapsed the graph sideways onto the y-axis, which portions would be covered?)
The function is defined for x = 2. So look at the function rule, find the half which is defined for x = 2, and plug 2 in for x in that half's rule.