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`

Note

  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.