Find a and b such that g(x) is continuous:

Question

g(x)={ -3x² -x + 41 if x < -3

{ ax + b if -3 <= x < 2

{ 2x³ -7x -28 if x> = 2

Answer 1

-3x^2 -x +41 = ax +b when x=-3

-3(9) +3 +41 = a(-3) +b

-3a + b = 17 ***equation 1

2x^3 -7x -28 = ax+b when x=2

2(8) -14 -28 =a(2) + b

2a + b = -26 ***equation 2

subtract equation 1 from equation 2 to eliminate one variable

5a = -43

a=-43/5 = -8.6

b = 17+3a = 17-3(8.6) = 17-25.8 =- 8.8

a=-8.6, b= -8.8

check the answers

x=2

ax+b = 2a +b = -17.2 -8.8 = -26

2(2)^3-7(2)-28 = 16-14-28= -=-26

x=-3

ax+b=3(8.6) -8.8=25.8-8.8= 17

-3(-3)^2 -(-3)+41 = -27+3+41= 17