Question

Which transformations would affect the starting point of a square root
function?

Answer 1

There are at least two transformations that would affect the starting point of a square root: (i) Horizontal translation, (ii) Vertical translation.

Explanation:

Let the square be represented by the following function:

`f(x) = √(x),\,\forall \,x \ge 0` (1)

Which means that function has only valid solutions for every element of
`x` greater or equal to 0. In particular, the starting point is
`x = 0`.

We can change the starting point of this function by horizontal translation, which is defined below:

`g(x) = f(x - a), \,\forall \,x \ge a` (2)

In other words, we create the resulting function:

`g(x) = √(x-a), \,\forall\,x \ge a` (3)

Another, possibility is using a vertical translation, whose definition is defined below:

`h(x) = f(x)+c,\,\forall \,x \ge 0` (4)

In other words, we create the following function:

`h(x) = √(x) +c` (5)

Hence, there are at least two transformations that would affect the starting point of a square root: (i) Horizontal translation, (ii) Vertical translation.