The first thing we can do is sketch the function, x^2 +3 is just the simple graph x^2 shifted 3 upward, using our knowledge of trnsformations...
x^2:
graph{x^2 [-10, 10, -5, 5]}
x^2 + 3 :
graph{x^2+3 [-9.375, 10.625, -1.56, 8.44]}
Hence to find the domain we must consider what values of x will give out a real number of y, what values the graph is valid for, looking at the graph, we see that all values of x gives a value for y, hence:
color(red)("Domain" : x in RR
As we know x^2 gives a vlaue for all values, possitive and negative
Now to consider the range, we just nned to aks what are all the values that y can take on, we see the smallest value of is # y = 3, and all the other values of y# above also can be found..
color(red)( "Range" : y>=3 )
