Write a formula for the piecewise function graphed in the fi

Write a formula for the piecewise function graphed in the figure. You should assume that if the graph has no endpoint marked (and continues to the edge of the picture) then it continues in this fashion without end. The formula for the left piece of f(x) is f(x) = for all x that satisfy the inequality The formula for the right piece of f(x) is f(x) = for all x that satisfy the inequality

Solution

a) Left side function : Two point sgiven ( 3, 5) and ( 4, 2)

slope = ( 2-5)/(4-3) = -3

y = -3x + c.find c using any1 point :

5 = -9 +c---> c = 14

f(x) = -3x +14 for x <= 4 ( -inf , 4]

b) Right side ; two point given ( 4, 8.5) and ( 6, 3)

slope = ( 3 - 8.5)/( 6-4) = - 5.5/2 = -2.75

y = -2.75x +c . find c using ( 6, 3)

3 = -16.5 +c ----> c = 19.5

f(x) = -2.75x + 19.5 for x > 4

f(x) = -2.75x +19.5 for ( 4 , infinity )