https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/functions-continuous-on-all-numbers 2026-06-25T15:40:55.094699315Z Determining if functions are continuous on all real numbers Discover how to determine if a function is continuous on all real numbers by examining two examples: eˣ and √x. Generally, common functions exhibit continuity within their domain. Explore the concept of continuity, including asymptotic and jump discontinuities, and learn how to identify continuous functions in various scenarios. video https://cdn.kastatic.org/googleusercontent/1Aulu_hV7y2jUnlDX-1viZ_T7Zym7gD4LmeO_UnbJs_X1t4MbYfTPbZArI5O_MoKLXATgLz5KFbjFDHNLRrAXUU Determining if functions are continuous on all real numbers Discover how to determine if a function is continuous on all real numbers by examining two examples: eˣ and √x. Generally, common functions exhibit continuity within their domain. Explore the concept of continuity, including asymptotic and jump discontinuities, and learn how to identify continuous functions in various scenarios. https://cdn.kastatic.org/ka-youtube-converted/DCWeH62w-NA.mp4/DCWeH62w-NA.mp4 197 Confirming continuity over an interval https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/functions-continuous-on-specific-numbers 2026-06-25T15:40:55.094699315Z Determining if functions are continuous at specific x-values Determine the continuity of two functions, ln(x-3) and e^(x-3), at x=3. Explore the concept of continuity, highlighting that common functions are continuous within their domain. Discover that ln(x-3) is not continuous at x=3, while e^(x-3) is continuous for all real numbers, including x=3. video https://cdn.kastatic.org/googleusercontent/JAKT4GFObH-3Fbgbk3sEl8xh4QoQ4oCBG3Vo7OuzJOXFsHbaKWB0dXm0yUu_3qgeHXFvnNvXfikfnBi-JiSJDB0 Determining if functions are continuous at specific x-values Determine the continuity of two functions, ln(x-3) and e^(x-3), at x=3. Explore the concept of continuity, highlighting that common functions are continuous within their domain. Discover that ln(x-3) is not continuous at x=3, while e^(x-3) is continuous for all real numbers, including x=3. https://cdn.kastatic.org/ka-youtube-converted/X51CaI4tfQg.mp4/X51CaI4tfQg.mp4 262 Confirming continuity over an interval https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/e/continuous-functions 2026-06-25T15:40:55.094699315Z Continuity and common functions Identify functions that are continuous for all real numbers, or for specific x-values. Tomer Gal exercise