Graph the function shown below fx x 3 Choose the correct

Graph the function shown below. f(x) = - [x] + 3 Choose the correct graph.

Solution

[x] means greatest integer function (usually), it returns the value of greatest integer below given number, i.e, the floor of given number. - sign in front of it makes the graph downward sloping, and +3 pushes this graph up by 3 units.

This makes both (A) and (B) eligible.

1) you can verify by plugging value x = 0, y = 3 (marked by solid blue dot, not the empty one)

2) you can try x = 0.5, y = - [0] + 3 = 3, which is given by option (B) the correct answer.

Note: If author meant [x] as least integer function, option A would be correct.