Question

The graph below belongs to which function family ?

Answer 1

This is an absolute value function.

Answer 2

Answer:

The graph belongs to a family of:

            Absolute value function.

Step-by-step explanation:

• We know that the graph of a linear function is a straight line which is increasing or continuously decreasing depending on the slope of a line.

whereas in the given graph the graph is first increasing and then decreasing i..e. it changes it's behavior.

               Hence, the given graph is not a graph of a linear function.

• Also, the graph of a quadratic function is in the shape of a parabola ; which is not a case here.

                    Hence, the graph is quadratic.

• The graph of a cubic function is in the shape of a curve which has end behavior in the opposite direction ( i.e. the behavior when x tends to infinity in both the directions)

But here the end behavior of the graph is in the same direction.

                Hence, it is not a graph of a cubic function.

So, we are left with Absolute value function.

• Since. we know that the graph of a absolute value function is such that it either attains a maximum or a minimum at a point and the graph first increases then decreases or first decreases and then increases respectively such that the shape of the graph is linear before and after it attains maximum or minimum.

Hence, the graph represents a absolute value function.