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Continuity of Functions

Continuity of Functions

At a Glance - Determining Continuity

When we say a function f is continuous, we usually mean it's continuous at every real number. In other words, it's continuous on the interval (-∞, ∞).

Some examples of continuous functions that are continuous at every real number are: polynomials, ex, sin(x), and cos(x).

If we add, subtract, multiply, or compose continuous functions, we find new continuous functions. If we take a quotient of continuous functions , this quotient will be continuous on any intervals that do not include places where g is zero. The quotient won't be defined there.

Example 1

Let f(x) = 4x2 + 3x and g(x) = sin(x). Determine whether each function is continuous. If not, where is the function discontinuous?

  • (f + g)
  • (fg)

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