## What are features of a function?

Key

**features**include: intercepts; intervals where the**function**is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.## What are the six key features you look for in a function?

**Key features**include: intercepts; intervals where the

**function**is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Relate the domain of a

**function**to its graph and, where applicable, to the quantitative relationship it describes.

## What is a mathematical function?

**Function, in mathematics**, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

**Functions**are ubiquitous in

**mathematics**and are essential for formulating physical relationships in the sciences.

## What makes a function 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. This is a**function**since each element from X is related to only one element in Y.## What is a 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.## How do you describe a function?

A

**function**is a relation in which each possible input value leads to exactly one output value. We say “the output is a**function**of the input.” The input values make up the domain, and the output values make up the range.## What is a function in your own words?

more A special relationship where each input has a single output. It is often written as “f(x)” where x is the input value. Example: f(x) = x/2 (“f of x equals x divided by 2”)

## What are 5 ways to represent a function?

**Key Takeaways**

- A
**function**can be**represented**verbally. For example, the circumference of a square is four times one of its sides. - A
**function**can be**represented**algebraically. For example, 3x+6 3 x + 6 . - A
**function**can be**represented**numerically. - A
**function**can be**represented**graphically.

## How do you explain if a graph is a function?

Use the vertical line test to

**determine whether**or not a**graph**represents a**function**.**If**a vertical line is moved across the**graph**and, at any time, touches the**graph**at only one point, then the**graph is a function**.**If**the vertical line touches the**graph**at more than one point, then the**graph**is not a**function**.## How can you say that a graph is a function?

Inspect the

**graph**to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the**graph**does not represent a**function**. If no vertical line can intersect the curve more than once, the**graph**does represent a**function**.## How do you write a function?

You

**write functions**with the**function**name followed by the dependent variable, such as f(x), g(x) or even h(t) if the**function**is dependent upon time. You read the**function**f(x) as “f of x” and h(t) as “h of t”.**Functions**do not have to be linear. The**function**g(x) = -x^2 -3x + 5 is a nonlinear**function**.## 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.## Is a circle a function?

No, a

**circle**is a two dimensional shape. 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.## How can you identify a function?

## Is a line a function?

If any vertical

**line**intersects a graph more than once, the relation represented by the graph is not a**function**. Notice that any vertical**line**would pass through only one point of the two graphs shown in parts (a) and (b) of Figure 13. From this we can conclude that these two graphs represent**functions**.## Are ellipses functions?

An

**ellipse**is not a**function**because it fails the vertical line test.## Is a straight line a function?

1 Answer. No, every

**straight line**is not a graph of a**function**. Nearly all linear equations are**functions**because they pass the vertical**line**test. The exceptions are relations that fail the vertical**line**test.## Are ellipses and hyperbolas functions?

Your very question–“Why is an

**ellipse**not a**function**?” shows it. When read precisely, the obvious way to answer this question is, “Because an**ellipse**is a kind of curve, and a**function**is [to use your words] just input and output values.”David Nilsen is the former editor of Fourth & Sycamore. He is a member of the National Book Critics Circle. You can find more of his writing on his website at davidnilsenwriter.com and follow him on Twitter as @NilsenDavid.