Lucius Romp asked, updated on September 29th, 2021; Topic:
graph

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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.

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Along with it, how do you know if it is a function or not?

A WAY easier (and faster), **way to know if it is a function** is to see **if** there are two of the same x-intercept (which make a vertical line). **If** there is, then it is **NOT** a **function**.

Not to mention, how do you tell if a graph is a function or relation? A **relation** where each element in the domain corresponds to exactly one element in the range. **If** any vertical line intersects the **graph** more than once, then the **graph** does not represent a **function**. The notation f(x)=y, which reads “f of x is equal to y.” Given a **function**, y and f(x) can be used interchangeably.

In the overall, how can you identify a function?

How do you tell if something is a function without graphing?

**If** a vertical line crosses the relation on the **graph** only once in all locations, the relation is a **function**. However, **if** a vertical line crosses the relation more than once, the relation is **not** a **function**. Using the vertical line test, all lines except for vertical lines **are functions**.

A **function** is a relation in which each input has only one output. : y is a **function** of x, x is **not a function** of y (y = 9 has multiple outputs). ... : y is **not a function** of x (x = 1 has multiple outputs), x is **not a function** of y (y = 2 has multiple outputs).

A **circle** is a set of points in the plane. A **function** is a mapping from one set to another, so they're completely different kinds of things, and a **circle** cannot be a **function**.

Defining the **Graph** of a **Function**. The **graph** of a **function** f is the set of all points in the plane of the form (x, f(x)). We could also define the **graph** of f to be the **graph** of the equation y = f(x). So, the **graph** of a **function** if a special case of the **graph** of an equation. Example 1.

Horizontal Line Test

A relation has **an** input value which corresponds **to an** output value. When each input value has **one** and only **one** output value, that relation is a **function**. **Functions can** be written as ordered pairs, tables, or graphs.

A **linear function** is a function whose **graph** is a straight line. The line can't be vertical, since then we wouldn't have a function, but any other sort of straight line is fine.

x=±√y is **not a function** because for some x input (or in this case almost every x input), there are two different y outputs. x=±√y is still an **equation** and can still be graphed, but it is **not a function**. You can have a **function** x=√y **if** you refer only to the principal (positive) answer.

if you can draw any **vertical line** that intersects more than one point on the relationship, then it is **not a function**. This is based on the fact that a **vertical line** is a constant value of x, so if there is one input, x, with more than two outputs, y, then it breaks the **function** rule.

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