Question

How do you write an equation for `y=sinx` translated 3.2 units to the right?

Answer 1

`sin(x-3.2)`

Explanation:

In graph transformation, there are three different transformations: translation, stretching and reflection. A general rule is that if the transformation comes within the brackets of `f(x)`, it will affect the `x`-values and if it appears outside the brackets then it will affect the `y`-values.

Graph transformations:
`1.` `f(x+a)` translates to the left by `a` units.
`2.` `f(x)+a` translates the graph up by `a` units
`3.` `f(kx)` stretches the graph horziontally by `k^(-1)`
`4.` `kf(x)` stretches the graph vertically by `k`
`5.` `f(-x)` reflects the graph in the line `x=0`
`6.` `-f(x)` reflects the graph in the line `y=0`