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# Advanced Math/Continuity of a piecewise function

Question
the function f is defined by f(x) = 2x-2  if  x<-1
Ax+B  if  -1≤x≤1
5x+7  if  x>1
Determine the values of A and B if f is continuous on all real numbers (R)

Questioner:   angelique
Country:   Gauteng, South Africa
Private:   No
Subject:   continuity of a function
Question:   the function f is defined by f(x) = 2x-2  if  x<-1
Ax+B  if  -1≤x≤1
5x+7  if  x>1
Determine the values of A and B if f is continuous on all real numbers (R)
.....................................
A piecewise function (that is what you see here) has these features:

1. It has pieces (duhhhh!, or whatever they say in SA.)  Each piece has its own RULE.
2. It has breakpoints - the boundary numbers between the pieces.

In this example, the pieces are:

Left:   (.. to -1)   RULE:  2x-2
Middle: (-1 to 1)          Ax+B
Right:  (1 to ..)          5x+7

and the breaks at:  x = -1, x = 1.

CONTINUITY PRINCIPLE:

The value at a breakpoint must be the same whether you use the rule to the left of the break or the rule to the right of the break.

So f(-1) must be the same whether you use 2x-2 or Ax+B.
and f(1) must be the same whether you use Ax+B or 5x+7.

Does that give you the clue?

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