Practice Continuous Function in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A function is continuous at a point if the limit equals the function value there, with no jumps, holes, or vertical asymptotes in the interval of interest.

A continuous function can be drawn without lifting the pencil — there are no sudden jumps, gaps, or points that shoot to infinity.

Example 1

easy
Show that f(x) = 3x^2 - 5x + 2 is continuous at x = 1 using the three-part definition of continuity.

Example 2

hard
Find where f(x) = \dfrac{x^2 - 4}{x - 2} is discontinuous, classify the discontinuity, and determine if it can be removed.

Example 3

easy
Is g(x) = \dfrac{1}{x} continuous on (-\infty, \infty)? If not, identify where and why.

Example 4

medium
Apply the Intermediate Value Theorem to show that h(x) = x^3 - x - 1 has a root in the interval [1, 2].
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