Question

How do you graph `y=-3absx`?

Answer 1

The objective of equations like this is to cause you to think about what the equations are actually doing. Take each part and consider them separately then put them together to see how the whole behaves.

Explanation:

This is a variant of equation type `y=x`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "y=-3|x|`

The equation part `|x|` is called 'absolute' `x`.

The value of `x` can be positive or negative but by turning it into an 'absolute' value it is always considered as positive.

Thus `-3|x|` will always be negative no matter what the value of `x` is. Apart from `x=0`. Think of 0 as sitting on the fence between positive and negative. You could say that 0 is neither positive nor negative.

So `y=-3|x| <=0`

The general shape of the graph is `^^`

When `x=0" "y=0` So the shape `^^` is symmetrical about the y-axis.