f(x) = ax + 3 if x > 2,
f(x) = x + 5 if -2 <= x <= 2,
f(x) = 8x + b if x < -2
Find a + b if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).
+130068 Set the first two equations equal
ax + 3 = x + 5
Let x = 2
2a + 3 = 2 + 5
2a + 3 = 7
2a = 7 - 3
2a = 4
a = 4/2 = 2
Set the second and third equations equal
x + 5 = 8x + b
Let x = - 2
-2 + 5 = 8(-2) + b
3 = -16 + b
b = 16 + 3 = 19
So the sytem that makes these continuous is
y= 2x + 3 ( x > 2)
y = x + 5 [ -2, 2 ]
y = 8x + 19 ( x < -2 )
a + b = 2 + 19 = 21
See the graph here : https://www.desmos.com/calculator/ywwaz4mykn
