Question

Find an equation for the graphed function below by using transformations of the graph of a toolkit function.

Answer 1

In order to find the equation, let's use the parent function f(x) = |x|, which has the following graph:

Then, looking at the given graph, we can see that the lowest point is at (-3, 4), and the parent function has the lowest point at (0, 0).

So, in order to translate the parent function into the given function, we need a translation of 3 units left and 4 units up.

A translation of 3 units left can be written as an increase in the value of x by 3 units:

`f^(\prime)(x)=|x+3|`

Then, a translation of 4 units up can be written as an increase in the value of f'(x) by 4 units:

`g(x)=|x+3|+4`