Question

(03.01) Is the following relation a function? y equals the sine of 3 x

Answer 1

Answer:

Yes. This is a function.

Step-by-step explanation:

Given is a function as

$y = sin 3x$

We find that for every x in the domain of real numbers there is a unique image for every x as sin 3x.

Thus this relation given satisfies the requirements of a function.

Also we find that this function is periodic with amplitude 1 and period = 2pi/3

So vertical line test if done will find that there is only one intersection for every vertical line throughout the domain

Hence this relation is definitely a function

Answer 2

A relation is a function if it passes the vertical line test.  That graph in a coordinate plane is just a sin wave that is spread out.  If you run a perfectly vertical line through the graph at every place on the graph, the line you draw will only go through the graph at one place every time.  That makes it a function.  It's not a one-to-one function cuz it fails the horizontal line test, but it is a function!