Domain & Range Revision Checklist

Set of all possible input values (x-values) for which the function is defined.

Set of all possible output values (y-values) that the function can produce.

Each input maps to exactly one output. One input → One output.

$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$

$f(x) = \sqrt{g(x)}$

$f(x) = \frac{P(x)}{Q(x)}$

$f(x) = ax^2 + bx + c$

$f(x) = \sin x$

$f(x) = \cos x$

$f(x) = \tan x$

$f(x) = \sin^{-1} x$ or $\arcsin x$

$f(x) = \cos^{-1} x$ or $\arccos x$

$f(x) = \tan^{-1} x$ or $\arctan x$

$f(x) = a^x$ where $a > 0, a \neq 1$

$f(x) = \log_a x$ where $a > 0, a \neq 1$

$f(x) = |x|$

$f(x) = [x]$ or $\lfloor x \rfloor$

$f(x) = \{x\} = x - [x]$

• Start from innermost function and work outward
• Handle each constraint separately
• Combine constraints using intersection
• Check edge cases and boundary values

• Forgetting to reverse inequality when multiplying by negative
• Missing denominator constraints in rational functions
• Overlooking square root constraints
• Confusing domain and range of inverse trig functions

• Test boundary values in the original function
• Check if domain makes all operations valid
• Verify range by considering function behavior at extremes
• Use graphical intuition when possible

• Memorize common function domains and ranges
• Recognize patterns in composite functions
• Use symmetry properties when applicable
• Practice mental calculation of simple cases