Question

How do you write an equation for `y=cosx` translated pi units to the left?

Answer 1

`y=cos(x+pi)`

Explanation:

We want to translate the graph in the x-direction, so our final equation should look like:

`y=cos(x-b)`

Where `b` is the number of units translated.
We are translating the graph `pi` units to the left, so `b` should be equal to `-pi`. Therefore, our final equation should look like:

`y=cos(x-(-pi))`

`y=cos(x+pi)`

If we graph the original and translated graph, we can see the difference:

Original:
graph{cos(x) [-10, 10, -5, 5]}

Translated:
graph{y=cos(x+pi) [-10, 10, -5, 5]}

You can see the y intercept for the original equation, `(0,1)`, has been translated to the left `pi` units, to `(-pi, 1)`. Hope this helps!