4 6 functions of two variables
Transcript of 4 6 functions of two variables
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4-6 FUNCTIONS OF TWO VARIABLESObjectives:1. Interpret graphs of two-variable functions2. Graph functions of two variables.
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FUNCTIONS OF TWO VARIABLESThe perimeter of a rectangle,
P = 2L + 2W is a function of two variables, L and W.
Can be written: P(L, W) = 2L + 2W
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GRAPHSType 1:Curves for constant values of W or L.
For constant w:P(L, 1) = 2L + 2P(L, 2) = 2L + 4 P(L, 3) = 2L + 6
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Type 2:Curves for constant values of P.
For example:P(L, W) = 8 when (L, W) = (1, 3), (2, 2), and (3, 1)
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EXAMPLE 1 If $100 is invested at an interest rate r compounded
annually, the amount t years later is A is a function of
_____ and _____ . The graph shows A vs. t
for constant r. What arethe equations of the 3 curves?
About how long does it take to double your money at each interest rate?
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EXAMPLE 2If find:f(3, 4)f(-4, 3)f(0, 5)List more pairs (x, y) for which
f(x, y) = 5