Variation and Graphs

Question Answer
Direct-Variation function A function with a formula of the form y=kx^n with k not equal to 0 and n>0
Z=kw^n Z=80 w=2, find Z when w=3 80=k(2^4)
80=k(16)
k=5
z=5w^4
z=5(3^4)
=5(81)
z=405
Inverse-variation function A function with a formula of the form y=k/x^n with k not equal to 0 and n>0
Inverse-variation example d=k/w
2=k/55
110=k
d=110/w
w=50
d=110/50
d=2.2
Slope -change in vertical distance/ change in forizontal distance
-change in dependent variable/ change in independent variable
-rise/run
Rate of change r1= (20,25)(40,100)
100-25/ 40-20= 75/20= 3.75
r2= (40,100)(60,225)
225-100/60-40=125/20=6.25
Graphs y=k/x k>0 quardrants: 1 & 3.
y=k/x k<0 quadrants: 2 & 4.
y=k/x^2 k>0 quadrants: 1 & 2.
y=k/x^2 k<0 quadranst: 3 & 4.

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