# How to create a piecewise function

### How do you create a piecewise function?

A

**piecewise function**is a**function**built from pieces of different**functions**over different intervals. For example, we can**make a piecewise function**f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.### How do you write a piecewise function from a word problem?

### How do you write a piecewise function in Google Docs?

### How do you find a piecewise function from a graph?

### How do you find the slope of a piecewise function?

### How do you find a function on a graph?

### What is a function rule for a graph?

A

**function**is a relation where there is only one output for every input. In other words, for every value of x, there is only one value for y.**Function Rule**. A**function rule**describes how to convert an input value (x) into an output value (y) for a given**function**. An example of a**function rule**is f(x) = x^2 + 3.### What is a function in a graph?

The

**graph**of the**function**is the set of all points (x,y) in the plane that satisfies the equation y=f(x) y = f ( x ) . If we can draw any vertical line that intersects a**graph**more than once, then the**graph**does not define a**function**because that x value has more than one output.### Whats a function and not a function?

A

**function**is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are**not functions**violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range. Example 4-1.### What is not a function?

A

**function**is a relation in which each input has only one output. In the relation , y is a**function**of x, because for each input x (1, 2, 3, or 0), there is only one output y. : y is**not a function**of x (x = 1 has multiple outputs), x is**not a function**of y (y = 2 has multiple outputs).### What defines a function?

A technical definition of a

**function**is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. We can write the statement that f is a**function**from X to Y using the**function**notation f:X→Y.### What makes a set not a function?

A relation from a

**set**X to a**set**Y is called a**function**if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to. For example, consider the following**sets**X and Y. It’s still a**function**, it’s just**not**a one-to-one**function**.### Which set is a function?

A

**function**is a**set**of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a**set**of ordered pairs defines a**function**.### How do you tell if a set is a function?

How do you figure out

**if**a relation is a**function**? You could**set**up the relation as a table of ordered pairs. Then, test to see**if**each element in the domain is matched with exactly one element in the range.**If**so, you have a**function**!### Is it a function or not a function?

Any input-output chart where an input has two or more different outputs is

**not a function**. For example, if you see the number 6 in two different input spaces, and the output is 3 in one case and 9 in another, the relation is**not a function**.### How can you identify a function?

If all possible vertical lines will only cross the relation in one place, then the relation is a

**function**. This works because if a vertical line crosses a relation in more than one place it means that there must be two y values corresponding to one x value in that relation.### How do you know if a function is not a function?

### Is circle a function?

No. The mathematical formula used to describe a circle is an equation, not one function. For a given set of inputs a function must have at most one

**output**. A circle can be described with two functions, one for the upper half and one for the lower half.### Is a line a function?

The vertical line test can be used to determine whether a

**graph**represents a function. If we can draw any vertical line that intersects a**graph**more than once, then the**graph**does not define a function because a function has only one output**value**for each**input value**.### Is half a circle a function?

**Function**defined by a relation in the form f(x) = √r2–x2 or f(x) = − √r2–x2 where r is the radius of a

**circle**centered on the origin point.

### Are ellipses functions?

An

**ellipse**is not a**function**because it fails the vertical line test.### What are the 3 dots called?

Those

**three**little**dots**are**called**an ellipsis (plural: ellipses).### Why is hyperbola not a function?

The

**hyperbola**is**not a function**because it fails the vertical line test. Regardless of whether the**hyperbola**is a vertical or horizontal**hyperbola**