# Math - Continuity

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Determine the constants a and b so that the function f is continuous on the entire real line:

f(x) = 2 , x=<-1
ax + b , -1<x<3
-2 , x>=3

could someone help me with this question please? thank you.

• Math - Continuity -

For continuity at x=-1, ax + b must equal 2 at x=-1
Therefore -a + b = 2
For continuity at x=3, ax+b must equal -2 there.
Therefore 3a + b = -2

Solve those two equations in two unknowns for a and b.
4a = -4
a = -1
b = 2 + a = ?

• Math - Continuity -

THANK YOU!!

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