Question

If the original function () = 22 − 1 is shifted to the left 3 units to make the

function (), which expression would represent ()?

Answer 1

A horizontal translation is expressed by transforming

`f(x)\mapsto f(x+k)`

If
`k` is positive, the function is translated to the left. If
`k` is negative, the function is translated to the right.

So, a 3-units left shift is given by
`k=3`. So you have

`f(x)=2x^2-1 \implies f(x+3)=2(x+3)^2-1`