Consider the function h(x)= x^ 2 -4x+3 x^ 2 -5x+6

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the function h(x)=x2−4x+3x2−5x+6.h(x)=\frac{x^{2}-4x+3}{x^{2}-5x+6}. Which of the following lists all real numbers at which hh is discontinuous and correctly classifies each type of discontinuity? (a) x=1 (removable),  x=2 (infinite)x=1\,(\text{removable}),\; x=2\,(\text{infinite}) (b) x=2 (infinite),  x=3 (removable)x=2\,(\text{infinite}),\; x=3\,(\text{removable}) (c) x=2 (removable),  x=3 (infinite)x=2\,(\text{removable}),\; x=3\,(\text{infinite}) (d) x=2 (infinite),  x=3 (infinite)x=2\,(\text{infinite}),\; x=3\,(\text{infinite})

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