The domain of a rational function is all real numbers except the values that make the original denominator zero. This rule is applied before simplifying or canceling factors.
⚠Do not use the simplified denominator alone. A canceled denominator factor still creates a domain restriction in the original function.
What This Calculator Checks
Denominator Zeros
Solves the denominator equation to find values excluded from the domain.
Interval Notation
Shows how the allowed real-number intervals are split by the excluded value.
Constant Denominator
If the denominator is a nonzero constant, the domain is all real numbers.
Graph Meaning
Excluded values become vertical asymptotes or holes depending on factor cancellation.
Teaching Example: for (2x-4)/(3x-6), solve 3x-6=0. The excluded value is x=2, so the domain is all real x except 2.
Frequently Asked Questions
How do you find the domain of a rational function?▼
Set the denominator not equal to zero and exclude every x-value that makes the denominator zero.
Do canceled factors still affect the domain?▼
Yes. If a factor cancels, the original function still excludes the zero of that factor, creating a hole.
Can a rational function have all real numbers as its domain?▼
Yes, if the denominator never equals zero or if the denominator is a nonzero constant.
What notation should I use for domain restrictions?▼
You can write set notation such as all real x except a value, or interval notation such as (-infinity,a) union (a,infinity).
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