October 16, 2009
ReTest Monday
1. Domain/Range
2. Analyze a Function
(domain/range/asymptotes, symmetry, boundedness)
3. Even/Odd
4. (fog)(x) and domain
5. Inverse Function and What the Graph looks like.
6. Transformations
October 16, 2009
October 16, 2009
October 16, 2009
2.2
Power Functions
f(x) = k xa
power
k and a are nonzero constants
constant
of variation
Examples:
circumference
C = 2πr
area
A = πr2
force of gravity F = k
d2
Boyle's Law
V=k
P
Power
Constant of Variation
October 16, 2009
direct variation: power functions with positive powers
inverse variation: power functions with negative powers
Write the statement as a power function equation.
1. The volume, V, of a circular cylinder with fixed height
is proportional to the square of its radius, r.
2. The speed of the current in a whirlpool varies
inversely with the distance from the whirlpool's center.
October 16, 2009
State the power and constant of variation for the function,
graph it, and analyze it.
1. f(x) = -3x3
2. g(x) = 1
x2
domain:
domain:
range:
range:
continuity:
continuity:
inc/dec behavior:
inc/dec behavior:
symmetry:
symmetry:
boundedness:
boundedness:
local extrema:
local extrema:
asymptotes:
asymptotes:
October 16, 2009
Monomial Function:
f(x) = k
or
f(x) = k xn
k is a constant and n is a postive integer
Examine the graphs.
1. y = xn (n is even)
2. y = x
n
(n is odd)
October 16, 2009
Sketch each graph.
1. f(x) = -x5
2. g(x) = x4 + 1
3. h(x) = -x4
October 16, 2009
Graphs of Power Functions
Graph the following:
1. y = x
2
2. y = x
3. y = x0.5
4. y = x(-0.5)
Graph 1-4 with a k-value of 3.
Graph 1-4 with a k-value of -3.
October 16, 2009
State the value of the constants k and a. Describe the
portion of the curve that lies in Quad. I or IV. Determine
whether f is even, odd, or undefined for x < 0. Describe the
rest of the curve, if any. Graph the function to see
whether it matches the description.
a. f(x) = 2x-3
b. f(x) = -x0.4
October 16, 2009
Use the data in Table 2.10 (pg 194) to obtain a power
function model for orbital period function of average
distance from the Sun. Then use the model to predict the
orbital period for Neptune, which is 4497 Gm from the Sun
on average.