Domain: The function

f(x) = x2 + 2

is defined for all real values of x (because there are no restrictions on the value of x).

Hence, the domain of `f(x)` is

"all real values of x".

Range: Since x2 is never negative, x2 + 2 is never less than `2`

Hence, the range of `f(x)` is

"all real numbers `f(x) ≥ 2`".

We can see that x can take any value in the graph, but the resulting y = f(x) values are greater than or equal to 2.

1 2 3 -1 -2 -3 1 2 3 4 5 6 7 8 9 10 -1 x f(x)
Range: `y>=2`
Domain: All `x`


  1. It is important to label the axes when sketching graphs. It helps with understanding what the graph represents.
  2. We saw how to sketch such graphs in Graph of a Function.