Question

Graph m(x) = |1/3x| Why is it a horizontal stretch? I don’t get it.

Answer 1

The easiest way to grap absolute values functions is to graph them on the positives x's and reflect it on the negatives.

We call a horizontal stretch on a function when we multiply the unknown (in this case, the x) by a number bigger than 0 but less than 1. In this case, we have 1/3:

`0<(1)/(3)<1`

Vertical and horizontal STRETCHING/SHRINKING

In a function, let's say h(x) = ax + b we could apply a vertical or horizontal transformation depending on what we multiply:

We can apply 2 types transformations: vertical ones or horizontal ones.

A horizontal transformation occurs when we multiply the x and not the entire function. Let's say that we want to apply a shrink of 3. Then we multiply the Unknown (x) by 3:

`h\mleft(x\mright)=ax+b\Rightarrow h(3x)=a(3x)+b`

But we can also apply a vertical transformation by multiplying the whole function and not just the x, like this:

`h\mleft(x\mright)=ax+b\Rightarrow3h\mleft(x\mright)=3(ax+b)`

This way you can see that if we multiply the x we get a horizontal transformation and if we multiply the whole function we get a vertical transformation

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Let's see the graph a the original function f(x) = |x|

Now let's apply a transformation by multiplying by 1/3 the x:

g(1/3x) = |1/3x|

If now we multiply x by 3, we get:

h(3x) = |3x|

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Red line: |x|

Green line: 1/2 |x|