Question

Let f(x) = √x, and let's call it the "base" function.Now, consider the function g(x) = √(x + 3) - 2. Imagine the graph that comes fromtransforming f(x) to g(x). Describe the transformations that have taken place.

Answer 1

There are two transformation that hapenned from f(x) to g(x): vertical and horizontal translation.

The horizontal translation affects the value of x, that is, you switch the variable x in the function by "x + k", where k is the value you are moving the function to the left or to the right.

In this case, we can see that the x inside the square root turns into a "x + 3", so we had a horizontal translation of 3 units to the left.

Then, a vertical translation is a transformation that affects the value of y, that is, the value of the function.

Comparing f(x) and g(x), we see that the value of f(x) was added by -2 (after the first transformation), so we had a vertical translation of 2 units down.

So the transformations are: translation 3 units to the left and translation 2 units down.