The Intermediate Value Theorem only guarantees a zero if the function changes sign (from positive to negative or vice versa) over an interval. If both y-values are positive or both are negative, a zero is not guaranteed because the function might stay above or below the axis without crossing it.
Conditions: The function is continuous.; The y-values at the endpoints of the interval have the same sign.
The Intermediate Value Theorem only guarantees a zero if the function changes sign (from positive to negative or vice versa) over an interval. If both y-values are positive or both are negative, a zero is not guaranteed because the function might stay above or below the axis without crossing it.
Conditions: The function is continuous.; The y-values at the endpoints of the interval have the same sign.