Let
f(x) = ax + 3 if x > 2
f(x) = x + 5 if -2 <= x <= 2
f(x) = 2x - b if x <= -2
Find a+b if the piecewise function is continuous
We can solve these two equations....
a(2) + 3 = 2 + 5 2(-2) - b = -2 + 5
2a + 3 = 7 -4 - b = 3
2a = 7 - 3 -4 - 3 = b
2a = 4 b = -7
a = 2
a + b = 2 - 7 = - 5
See the graph here : https://www.desmos.com/calculator/vqklkrnk5l
