4-6 FUNCTIONS OF TWO VARIABLESObjectives:1. Interpret graphs of two-variable functions2. Graph functions of two variables.

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

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

Type 2:Curves for constant values of P.

For example:P(L, W) = 8 when (L, W) = (1, 3), (2, 2), and (3, 1)

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?

EXAMPLE 2If find:f(3, 4)f(-4, 3)f(0, 5)List more pairs (x, y) for which

f(x, y) = 5