2.2 Notes.notebook
September 22, 2016
2.2 Power Functions with Modeling
Name: ________________
Objective: Students will be able to sketch power functions.
Power Function
Any function that can be written in the form f(x) = kxa, where k and
a are nonzero constants, is a power function. The constant a is the
power, and k is the constant of variation, or constant of proportion.
We say f(x) varies as the ath power of x, or f(x) is proportional to
the ath power of x.
Examples Determine whether the function is a power function.
If it's a power function, state the power and constant of variation.
1.) f(x) = π 32x
2.) F = k/d2
3.) A = πr2
Sep 15­4:12 PM
Monomial Function
Any function that can be written as f(x) = k or f(x) = k xn, where k
is a constant and n is a positive integer, is a monomial function.
Examples Determine whether the function is a monomial function.
1.) f(x) = 3x-2
2.) y = -2 5x
3.) A = lw, l constant
The power function formulas with positive powers are statements
of ________ ___________.
The power functions formulas with negative powers are
statements of ________ _________.
Sep 15­4:29 PM
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2.2 Notes.notebook
September 22, 2016
Examples 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 refractive index of a medium n is inversely proportional to the velocity of
the light in the medium, with c as the constant of velocity of light in free space.
Examples Write a sentence that expresses the relationship in the formula.
3.) C = πD, where C and D are the circumference and diameter of a circle and π
is the usual mathematical constant.
Sep 15­4:37 PM
Example State the power and constant of variation, graph it and
analyze it.
1.) f(x) = ∛x
Domain:
Range:
Continuity:
Increasing/Decreasing:
Symmetry:
Boundedness:
Extrema:
Asymptotes:
End Behavior:
Sep 15­4:44 PM
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2.2 Notes.notebook
September 22, 2016
Example State the power and constant of variation, graph it and
analyze it.
1.) f(x) = -2x-3
Domain:
Range:
Continuity:
Increasing/Decreasing:
Symmetry:
Boundedness:
Extrema:
Asymptotes:
End Behavior:
Sep 15­4:44 PM
Assignment: pages 196-199: #1-25 odd, 58-63
Sep 15­4:52 PM
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