Question

Express the function graphed on the axes below as a piecewise function.

Answer 1

Answer:

y = 2/3x +6  for x< -3

y = 2/3x +1     for x> 3

Step-by-step explanation:

The graph is a line for  x < -3

( - 6,2) and ( -3,4)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 4-2)/(-3 - -6) = 2/ ( -3+6) = 2/3

The slope is 2/3

Using point slope form

y-y1 = m(x-x1)  and the point ( -6,2)

y -2 = 2/3(x - -6)

y -2 = 2/3(x +6)

y-2 = 2/3 x +4

y = 2/3x +6 x< -3

The graph is a line for  x > 3

(3,3) and ( 6,5)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 5-3)/(6-3) = 2/ (3) = 2/3

The slope is 2/3

Using point slope form

y-y1 = m(x-x1)  and the point (6,5)

y -5 = 2/3(x - 6)

y-5 = 2/3 x -4

y = 2/3x +1   x> 3