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Rational Function Intercept Calculator

Find x-intercepts and y-intercepts of rational functions

R(x) = (x + ) / (x +)

Intercept Rules

x-intercept: numerator = 0 and denominator != 0

y-intercept: f(0), if denominator at x=0 is not zero

A canceled zero gives a hole, not an x-intercept

Intercepts mark where the graph crosses the coordinate axes. For rational functions, every intercept must also pass the domain check.

X-Intercept

Set the numerator equal to zero because a fraction equals zero only when its numerator is zero.

Y-Intercept

Substitute x=0 into the rational function if x=0 is allowed by the denominator.

Domain Check

If a candidate intercept makes the denominator zero, it is not a valid point on the graph.

Graph Sketching

Intercepts, asymptotes, and holes together give a quick rational graph outline.

Teaching Example: for (2x-4)/(3x+6), the x-intercept is x=2 because 2x-4=0 and the denominator is not zero. The y-intercept is -4/6 = -2/3.

Frequently Asked Questions

How do you find x-intercepts of a rational function?▼

Set the numerator equal to zero, then check that the denominator is not zero at those x-values.

How do you find the y-intercept?▼

Evaluate the function at x=0 if x=0 is in the domain.

Can an x-intercept be canceled?▼

Yes. If the numerator zero also makes the denominator zero and cancels, it becomes a hole, not an intercept.

Can a rational function have no y-intercept?▼

Yes. If the denominator is zero at x=0, the function is undefined there, so there is no y-intercept.

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