## How do you solve piecewise functions?

## How do you write piecewise formula?

## How do you graph a piecewise function on a calculator?

**Here are the steps to**

**graph a piecewise function**in your**calculator**:- Press [ALPHA][Y=][ENTER] to insert the n/d fraction template in the Y= editor.
- Enter the
**function**piece in the numerator and enter the corresponding interval in the denominator. - Press [
**GRAPH**] to**graph**the**function**pieces.

## How do you tell if a piecewise function is a function?

Mentor: Look at one of the graphs you have a question about. Then take a vertical line and place it on the graph.

**If**the graph is a**function**, then no matter where on the graph you place the vertical line, the graph should only cross the vertical line once.## How do you determine if a piecewise function is continuous?

At the endpoints, where two “pieces” come together. The

**piecewise function**f(x) is**continuous**at such a point**if**and only of the left- and right-hand limits of the pieces agree and are equal to the value of the f.## When do we use piecewise function?

**We use piecewise functions**to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” For example,

**we**often encounter situations in business for which the cost per piece of a certain item

**is**discounted once the number ordered exceeds a certain value.

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

If they are equal the

**function**is**continuous**at that point and if they aren’t equal the**function**isn’t**continuous**at that point. First x=−2 x = − 2 . The**function**value and the limit aren’t the same and so the**function is not continuous**at this point.## What are the 3 conditions of continuity?

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.

## Which function is always continuous?

The most common and restrictive definition is that a

**function**is**continuous**if it is**continuous**at all real numbers. In this case, the previous two examples are not**continuous**, but every polynomial**function**is**continuous**, as are the sine, cosine, and exponential**functions**.## How do you make a function continuous?

## Can a function be differentiable but not continuous?

We see that if a

**function**is**differentiable**at a point, then it must be**continuous**at that point. 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 .## How do you determine if a function is continuous and differentiable?

**If**f is

**differentiable**at x=a, then f is

**continuous**at x=a. Equivalently,

**if**f fails to be

**continuous**at x=a, then f will not be

**differentiable**at x=a. A

**function**can be

**continuous**at a point, but not be

**differentiable**there.

## Is every continuous function is 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.## Is every continuous function is 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**.

## Do all continuous functions have Antiderivatives?

Every

**continuous function has**an**antiderivative**, and in fact**has**infinitely many**antiderivatives**. Two**antiderivatives**for the same**function**f(x) differ by a constant.## Does every function have a limit?

Some

**functions do**not**have**any kind of**limit**as x tends to infinity. For example, consider the**function**f(x) = xsin x. This**function does**not**get**close to any particular real number as x gets large, because we can always choose a value of x to make f(x) larger than any number we choose.## Can 0 be a limit?

When simply evaluating an equation

**0**/**0**is undefined. However, in take the**limit**, if we get**0**/**0**we**can**get a variety of answers and the only way to know which on is correct is to actually compute the**limit**. Once again however note that we get the indeterminate form**0**/**0**if we try to just evaluate the**limit**.## Where does the limit not exist?

A common situation where the

**limit**of a function**does not exist**is when the one-sided**limits exist**and are**not**equal: the function “jumps” at the point. The**limit**of f f f at x 0 x_0 x0**does not exist**.## Does limit exist at a hole?

The

**limit**at a**hole**: The**limit**at a**hole**is the height of the**hole**. is undefined, the result would be a**hole**in the function. Function**holes**often come about from the impossibility of dividing zero by zero.