Question

Write a new function that represents a transformation to the parent function if the new function shifts right 5 units and up 3 units.​

Answer 1

Let's define two transformations.

Vertical translation.

If we have a function f(x), a vertical translation of N untis is written as:

g(x) = f(x) + N

If N is positive, then the translation is upwards

If N is negative, then the translation is downwards.

Horizontal translation.

If we have a function f(x), a horizontal translation of N units is written as:

g(x) = f(x - N)

if N is positive, then the translation is to the right

If N is negative, then the translation is to the left.

Now we have a function g(x) that is a transformation of a parent function f(x) (we actually do not know which parent function, so i assume f(x) = x^2) such that we have a shift right 5 units and up 3 units.

Then:

g(x) = f(x - 5) + 3

and again, using f(x) = x^2

g(x) = (x - 5)^2 + 3