**Figure \(\PageIndex{6}\) illustrates the differences in. **

**Figure 6 illustrates the differences in these types of. **

**. We saw in the previous section that a function could have a left-hand limit and a right-hand limit even if they are not equal. **

**II. **

**The function f (x) = x − 7 |x − 3| − 4 is not continuous at x = −1. **

**. Below figure shows the graph of a continuous function. the function doesn’t go to infinity). **

**In this discontinuity, the two sides of the graph will reach two different y-values. **

**Sep 7, 2022 · Intuitively, a removable discontinuity is a discontinuity for which there is a hole in the graph, a jump discontinuity is a noninfinite discontinuity for which the sections of the function do not meet up, and an infinite discontinuity is a discontinuity located at a vertical asymptote. The function f (x) = x − 7 |x − 3| − 4 is not continuous at x = −1. . **

**. Look out for holes, jumps or vertical asymptotes (where the function heads up/down towards infinity). **

**Intuitively, a removable discontinuity is a discontinuity for which there is a hole in the graph, a jump discontinuity is a noninfinite discontinuity for which the sections of the function do not meet up, and an infinite discontinuity is a discontinuity located at a vertical asymptote. **

**Here is a continuous function: Examples. **

**There are basically two types of discontinuity: Infinite Discontinuity; Jump Discontinuity; Infinite Discontinuity. . **

**The function f (x) = x − 7 |x − 3| − 4 is not continuous at x = −1. The function tanx is not continuous, but is continuous on for example the interval −π/2 < x < π/2. **

**Glossary**

**continuous**function a function that has no holes or breaks in its graph discontinuous function a function that is not**continuous**at [latex]x=a[/latex]**jump****discontinuity**.**This calculus video tutorial provides a basic introduction into to continuity. **

**Jump Discontinuity** To understand **discontinuity**, you should know what is **continuity** of a function.

**Graphically, a discontinuous function will either have a hole—one spot, or several spots, where the function is not defined—or a jump, where the value of f. Sep 7, 2022 · Intuitively, a removable discontinuity is a discontinuity for which there is a hole in the graph, a jump discontinuity is a noninfinite discontinuity for which the sections of the function do not meet up, and an infinite discontinuity is a discontinuity located at a vertical asymptote. The graph of f has a jump discontinuity above x = −1. **

**A jump discontinuity. That is not a formal definition, but it helps you understand the idea. . Nov 16, 2022 · This kind of discontinuity in a graph is called a jump discontinuity. . This is also called Asymptotic Discontinuity. **

**. **

**II. Classify any discontinuity as jump, removable, infinite, or other. **

**Intuitively, a removable discontinuity is a discontinuity for which there is a hole in the graph, a jump discontinuity is a noninfinite discontinuity for which the sections of the function do not meet up, and an infinite discontinuity is a discontinuity located at a vertical asymptote. **

** The graph of the function will show a jump or gap between separate segments of the curve. **

**Proof (continued). **

**Intuitively, a removable discontinuity is a discontinuity for which there is a hole in the graph, a jump discontinuity is a noninfinite discontinuity for which the sections of the function do not meet up, and. **

**Since f is increasing, then f(x− 0) ≤ f(x+ 0). **

continuous, it cannot be left.