Question

Which graph represents the piecewise-defined function?

Answer 1

Last graph is the answer

when x >= 3 then y = 6
when 0<= x< 3 when y = -x + 4
so if
x = 2, y = -2 + 4 = 2
x = 1, y = -1 + 4 = 3
x = 0, y = 0 + 4 = 4

Answer 2

Answer with explanation:

We are given a piece-wise defined function as:

f(x)=  -x+4   when  0≤x<3

  and   6   when  x ≥ 3

Clearly we see that the graph between 0 and 3 is a line with a negative slope since the coefficient of x is negative and at x=0 we have f(x)=4

i.e. the graph starts at (0,4)

Also, the graph is discontinuous at x=3

Since the left hand and right hand limit is not equal at x=3

The left hand limit at x=3 is: 1

and the right hand limit at x=3 is: 6

also the value of function at x=3 is: 6

The graph is a horizontal line y=6 for x ≥ 3

and also there is a closed circle at (3,6)

and open at (3,1)

The correct graph is attached to the circle.