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- https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/02%3A_Limits/2.05%3A_ContinuityFor a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that p...For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite. A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/05%3A_Polynomial_and_Rational_Functions/5.06%3A_Rational_FunctionsIn the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables i...In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/02%3A_Learning_Limits/2.07%3A_ContinuityThis section introduces the concept of continuity in Calculus, explaining how a function is continuous at a point if the limit exists and equals the function's value at that point. It discusses the ty...This section introduces the concept of continuity in Calculus, explaining how a function is continuous at a point if the limit exists and equals the function's value at that point. It discusses the types of discontinuities (removable, jump, and infinite) and provides examples to illustrate these concepts. The section also covers the Intermediate Value Theorem, which relies on continuity to guarantee the existence of certain values within an interval.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/04%3A_Polynomial_and_Rational_Functions/4.06%3A_Introduction_to_Rational_FunctionsThe way we symbolize the relationship between the end behavior of \(y=g(x)\) with that of the line \(y=x-1\) is to write 'as \(x \rightarrow \pm \infty\), \(g(x) \rightarrow x-1\).' In this case, we s...The way we symbolize the relationship between the end behavior of \(y=g(x)\) with that of the line \(y=x-1\) is to write 'as \(x \rightarrow \pm \infty\), \(g(x) \rightarrow x-1\).' In this case, we say the line \(y=x-1\) is a slant asymptote of \(y=g(x)\).
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)/03%3A_Polynomial_and_Rational_Functions/3.06%3A_Introduction_to_Rational_FunctionsThe way we symbolize the relationship between the end behavior of \(y=g(x)\) with that of the line \(y=x-1\) is to write 'as \(x \rightarrow \pm \infty\), \(g(x) \rightarrow x-1\).' In this case, we s...The way we symbolize the relationship between the end behavior of \(y=g(x)\) with that of the line \(y=x-1\) is to write 'as \(x \rightarrow \pm \infty\), \(g(x) \rightarrow x-1\).' In this case, we say the line \(y=x-1\) is a slant asymptote of \(y=g(x)\).
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Kravets)/02%3A_Limits/2.04%3A_ContinuityFor a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that p...For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite. A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Reed)/02%3A_Limits/2.04%3A_ContinuityFor a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that p...For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite. A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/05%3A_Polynomial_and_Rational_Functions/5.06%3A_Rational_FunctionsIn the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables i...In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/04%3A_Polynomial_and_Rational_Functions/4.07%3A_Rational_FunctionsIn the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables i...In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator.
- https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/02%3A_Limits/2.05%3A_ContinuityFor a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that p...For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite. A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/02%3A_Limits/2.04%3A_ContinuityFor a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that p...For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite. A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
