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##### Asked by: Zhijie Ammersdorfer

science space and astronomy# How do you know when Y is a function of x?

Last Updated: 1st May, 2020

**know**that

**y is a function of x**becausefor each

**x**-coordinate there is exactly one

**y**-coordinate. If we draw a vertical line across the plot ofthe

**function**, it only intersects the

**function**oncefor each value of

**x**. Yes, this graph is a

**function**.

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Thereof, how do you know if Y is a function of x?

The Horizontal Line Test The **x** value of a point where a vertical lineintersects a **function** represents the input for that output**y** value. **If** we can draw any horizontal line thatintersects a graph more than once, then the graph does notrepresent a **function** because that **y** value has morethan one input.

Likewise, how do you know if something's not a function? ANSWER: Sample answer: You can **determine whether**each element of the domain is paired with exactly one element ofthe range. For example, **if** given a graph, you could use thevertical line test; **if** a vertical line intersects the graphmore than once, then the relation that the graph represents is**not a function**. 56.

Secondly, what does it mean when Y is a function of x?

The phrase "**y is a function of x**" **means**that the value of **y** depends upon the value of **x**, so:**y** can be written in terms of **x** (e.g. **y** = 3x ).If f(**x**) = 3x, and **y is a function of x** (i.e. **y**= f(**x**) ), then the value of **y** when **x** is 4 isf(4), which is found by replacing **x**"s by 4"s .

How do you determine whether the relation is a function?

**Determining whether** a **relation is afunction** involves making sure that for every input there isonly one output. In order for a **relation** to be called a**function**, each X value must have exactly one Y value. X hasto have exactly one Y value.