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Identify Removable, Jump, and Infinite Discontinuities
Worksheet
Grade Level
Pre-Calculus
Pre-CAL.189 Identify Removable, Jump, and Infinite Discontinuities
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Let f(x) = x
2
for x < -1 and f(x) = 1/(x + 1)
2
for x > -1. Which statement correctly describes the discontinuity at x = -1?
A
Removable discontinuity; a finite two-sided limit exists at x=-1, but the point is missing or changed.
B
Infinite discontinuity; the right-hand branch 1/(x + 1)
2
grows toward +infinity while the left branch approaches 1, so no finite two-sided limit exists.
C
Jump discontinuity; the one-sided limits are finite but unequal at x=-1.
D
Continuous at x=-1; the function value equals the limit.
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