Piecewise defined FUNctions

Given the function defined by:
f(x) = x² + bx, if x<2
f(x) = bx + c, if x ≥ 2

Determine the ordered triple (a, b, c) so that all of the following conditions are true:

1. f (x) is continuous
2. f (3) = 20
3.

lim f(x)

x→2

View the solution

Piecewise defined FUNctions Solution

The first statement allows us to say that a(2)² + b(2) = b(2) + c, which reduces to 4a = c.

The second statement allows us to say that b(3) + c = 20.

The third statement allows us to say that a(-2)² + b(-2) = 0, which reduces to 2a = b.

Substituting appropriately gives us the ordered triple (2, 4, 8).

What's the Value (or does it diverge?)

What's my equation?

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