Denition approach of learning new topics

2.4 Domain and range of a function 9
Example 2. Plot the graph of the function given as y = x 2 + 1
Plotting points and getting a rough idea of the graph.
Points (0, 1), (1, 2), (−1, 2), (2, 5), (−2, 5). So we get a rough idea of the graph
and what remains is to get the graph smooth.
2.4 Domain and range of a function
Denition. Domain (D f ):
All values that will be taken (input) by the function y = f(x) i.e. all values
of x that keeps the function well dened.
Denition. Range (R f ):
All values of y (output) that will be taken for all values of x ∈ D f i.e. y ∈ R f
i.e. R f = {y | y = f(x) such that x ∈ D f }
Example 3. Domain and range of the following functions
1. f(x) = 1 x
D f = R − {0}
R f = R − {0}
2. f(x) = √ x
D f : [0, ∞)
R f : [0, ∞) (since √ x is positive root of x)