H2 Maths Formulas, Techniques & Graphs >> Functions and Graphs >> Functions >>
Find range of a function by GC
Steps
Use the graphing calculator to sketch graph of the function (with domain entered)
The possible values of y is the range of the function
Example
$$ f : x \mapsto 1 + {1 \over x}, x \in \mathbb{R}, x \ne 0 $$
Graphing the function:
From the graph, $y$ can be any real value except $1$.
The range in set-builder notation is $$ R_f = \{ y \in \mathbb{R} \phantom{.} | \phantom{.} y \ne 1\} $$
The range in interval notation is $$ R_f = ( -\infty, 1) \phantom{.} \cup \phantom{.} (1, \infty) $$
An alternative presentation in interval notation is $$ R_f = \mathbb{R} \backslash \{1 \} $$
Example (with restricted domain)
$$ g : x \mapsto x^2 - 2x - 2, \phantom{000} x \in \mathbb{R}, x > -1 $$
Graphing in the GC:
Actual sketch:
From the graph, the smallest value of $y$ is $-3$ (minimum point).
The range in set-builder notation is $$ R_g = \{ y \in \mathbb{R} \phantom{.} | \phantom{.} y \ge -3 \} $$
The range in interval notation is $$ R_g = [-3, \infty) $$
More on Functions:
Functions
Inverse function
Composite functions
Other concepts (on Functions)