Question

How can I know when the graph represents a horizontal stretch or a horizontal translation? thank you

Answer 1

Stretches and translations

We know that tehre are some ways of transform the graph of a function:

we can mutiply (or divide) it by a number or add (substract) a number to it - among other operations.

Stretches: multiplications and divisions

When we divide or multiply the equation of a function we are going to be stretching it:

- if we multiply a number we stretch it vertically

- if we divide a number we stretch it horizontally

In this case

`f(x)=2g(x)`

It is a multiplication of g(x), then it is a vertical stretch of g(x).

Tranlations: additions and substractions

If we want to translate a function vertically we just must add or substract a number to the whole equation. For example:

If we want to translate it horizontally, then we have to add or substract a number to the x part of the equation: