Contents

- How do you know if a graph is continuous or discontinuous?
- What type of graphs are continuous?
- What does continuous look like on a graph?
- What makes a graph continuous but not differentiable?
- Does a graph have to be continuous to be differentiable?
- How do you know if a function is continuous but not differentiable?
- Where is the function continuous but not differentiable?
- Is every continuous function integrable?
- Is every continuous function differentiable?
- How do you know if a graph is not differentiable?
- Is a corner continuous?
- What does a concave up graph look like?
- How do you know when a function is continuous?
- What are the 3 conditions of continuity?
- Can a function be continuous and not differentiable?
- How do you know if something is discrete or continuous?
- Is number of days discrete or continuous?
- Is number of students discrete or continuous?

## How do you know if a graph is continuous or discontinuous?

A function being **continuous** at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable **discontinuity** is **when** the two-sided limit exists, but isn’t equal to the function’s value.

## What type of graphs are continuous?

This **type** of data is often represented using tally **charts**, bar **charts** or pie **charts**. **Continuous** data is data that can take any value. Height, weight, temperature and length are all examples of **continuous** data.

## What does continuous look like on a graph?

**Continuous graphs** are **graphs** that **appear** as one smooth **curve**, with no holes or gaps. Intuitively, **continuous graphs** are those that can be drawn without lifting a pencil. This is often the case when collecting ***continuous** data*, **like** the speed of a car at different times.

## What makes a graph continuous but not differentiable?

The absolute value **function** is **continuous** (i.e. it has **no** gaps). It is **differentiable** everywhere except at the point x = 0, where it **makes** a sharp turn as it crosses the y-axis. A cusp on the **graph** of a **continuous function**. At zero, the **function** is **continuous but not differentiable**.

## Does a graph have to be continuous to be differentiable?

If is not **continuous** at , then is not **differentiable** at . Thus from the theorem above, we see that all **differentiable** functions on are **continuous** on . Nevertheless there are **continuous** functions on that are not **differentiable** on .

## How do you know if a function is continuous but not differentiable?

## Where is the function continuous but not differentiable?

In mathematics, the Weierstrass **function** is an example of a real-valued **function that is continuous** everywhere **but differentiable** nowhere. It is an example of a fractal curve.

## Is every continuous function integrable?

**Continuous functions** are **integrable**, but continuity is not a necessary condition for **integrability**. As the following theorem illustrates, **functions** with jump discontinuities can also be **integrable**.

## Is every continuous function differentiable?

We have the statement which is given to us in the question that: **Every continuous function** is **differentiable**. Therefore, the limits do not exist and thus the **function** is not **differentiable**. But we see that f(x)=|x| is **continuous** because limx→cf(x)=limx→c|x|=f(c) exists for all the possible values of c.

## How do you know if a graph is not differentiable?

A function is **not differentiable** at a **if** its **graph** has a vertical tangent line at a. The tangent line to the curve becomes steeper as x approaches a until it becomes a vertical line. Since the slope of a vertical line is undefined, the function is **not differentiable** in this case.

## Is a corner continuous?

Cusps and **corners** are points on the curve defined by a **continuous** function that are singular points or where the derivative of the function does not exist. A **corner** is, more generally, any point where a **continuous** function’s derivative is discontinuous.

## What does a concave up graph look like?

## How do you know when a function is continuous?

**Concavity** relates to the rate of change of a function’s derivative. A function f is **concave up** (or upwards) where the derivative f′ is increasing. Graphically, a **graph** that’s **concave up** has a cup shape, ∪, and a **graph** that’s **concave** down has a cap shape, ∩.

## What are the 3 conditions of continuity?

## Can a function be continuous and not differentiable?

Saying a **function** f is **continuous when** x=c is the same as saying that the **function’s** two-side limit at x=c exists and is equal to f(c).

## How do you know if something is discrete or continuous?

Key Concepts. 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.

## Is number of days discrete or continuous?

**Continuous**. When a **function** is **differentiable** it is also **continuous**. But a **function can** be **continuous** but **not differentiable**.

## Is number of students discrete or continuous?

Definition: A set of data is said to be **continuous if** the values belonging to the set can take on ANY value within a finite or infinite interval. Definition: A set of data is said to be **discrete if** the values belonging to the set are distinct and separate (unconnected values).