Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Let the square be represented by the following function:

$f(x) = \sqrt{x},\,\forall \,x \ge 0$ (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:

$g(x) = \sqrt{x-a}, \,\forall\,x \ge a$ (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:

$h(x) = \sqrt{x} +c$ (5)

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