MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Let g be a real-valued function with g(1)=−5 and g(4)=3. The function is discontinuous at exactly one point in the interval (1,4). Which statement best describes what can be concluded about the equation g(x)=0 on (1,4)?
(a) A solution is guaranteed because the values at x=1 and x=4 have opposite signs.
(b) A solution is not guaranteed because the function is not continuous on the entire interval.
(c) No solution exists because the function is discontinuous at a point inside the interval.
(d) At least two solutions exist because the function changes sign and has a discontinuity.