Question

Which function is represented by this graph?

Answer 1

The last option is not even a function, because it ambiguously defines the endpoints.

The first option doesn't define the endpoint, because they are always excluded.

So, the correct option is the second one, because it includes the left endpoint and excludes the right one.

Answer 2

The function d(x) is given by:

d(x)= 1 if 1≤x<4

2 if 4≤x<6

3.5 if 6≤x<11

and 5 if 11≤x<13

Explanation:

• By looking at the graph of the function we observe that the function takes the value :

1 when 1≤x<4

( because the graph is a straight horizontal line i.e. y=1 and the line has a closed circle at x=1 and open circle at x=4 )

• also the function takes the value: 2 when 4≤x<6

( because the graph is a straight horizontal line i.e. y=2 and the line has a closed circle at x=4 and open circle at x=6 )

• also the function takes the value: 3.5 when 6≤x<11

( because the graph is a straight horizontal line i.e. y=3.5 and the line has a closed circle at x=6 and open circle at x=11 )

• also the function takes the value: 5 when 11≤x<13

( because the graph is a straight horizontal line i.e. y=5 and the line has a closed circle at x=11 and open circle at x=13 )