Question

In two or more complete sentences, define the key features of the graph below and explain how to write its equation using function notation.

Answer 1

The function notation of the graph is f(x) = |x-3| - 2

Explanation:

From the graph it is evident that it is the graph of the absolute value of the function i.e. f(x) = |x| and we know that 'Translation' is a transformation that shifts the graph of a function in any direction.

Now, as we can see that the graph is shifted towards the right of the y-axis at point x=3, this means that it is translated by 3 units to the right of y-axis.

Therefore, the function becomes f(x) = |x-3|.

Furthermore, it is also shifted downwards at the point x= -2, this means that it is translated by 2 units downward from the x-axis.

Hence, the new function is f(x) = |x-3| - 2.

It can also be seen from the figure below that the graph of above f(x) is same as that of the provided image.

Answer 2

The graph is a function of absolute value.
This means that for each value of f (x) there are two possible values of x.
The absolute value function is:
f (x) = lxl
y = f (x) - 2 shifts the graph 2 units down.
y = f (x + 3) moves the graph 3 units to the right.
Finally:
The function that best fits this graph is:
f (x) = l-x + 3l-2