The range of a function is the set of possible y values.
Replace x by each value of domain and solve for y:
f(x) = 2x+5
y=2x+5
x=-2
y= 2(-2)+5 = -4+5=1
x=-1
y= 2(-1)+5 = -2+5=3
x=0
y=2(0)+5=5
x=1
y=2(1)+5 = 2+5=7
x=2
y= 2(2)+5=4+5=9
Range: {1,3,5,7,9}