2.2 Power Functions with Modeling. Garth Schanock, Robert Watt, Luke Piltz. http://ichiko-wind-griffin.deviantart.com/art/Lame-Math-Joke. http://brownsharpie.courtneygibbons.org/?p=557. What is a Power Function?. f(x)=kx^a Where: k is the constant of variation or constant of proportion
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Garth Schanock, Robert Watt, Luke Piltz
Determine whether the function is a power function. If it is a power function, give the power and constant of variation.
Yes, it is a power function because it is in the form f(x)=k*xᵃ. The power, or a, is 4. The constant, or k, is 83.
Yes, this is a power function because it is in the form f(x)=k*xᵃ. The power is 0 and the constant is 13. Because anything to the power of zero is one, there isn't an x with the 13.
f(x)=k or f(x)=k*x^n
Determine whether the function is monomial. If it is, give the power and constant. If it isn't, explain why.
Yes, the function is a monomial. The power is 0 and the constant is -7.
No, this function is not a monomial function. It is not a monomial function because the power is not a positive integer.
f(x)=xⁿ is an even function if n is even
Ex. f(x)=3x⁶ f(x)=4x-⁶
f(x)=xⁿ is an odd function if n is odd
Ex. f(x)=3x⁵ f(x)=82x⁹
Write the statement as power function. Use k as the constant of variation if one is not specified.
1. The area A of an equilateral triangle varies directly as the square of the length s of its sides.
2. The force of gravity, F, acting on an object is inversely proportional to the square of the distance, d, from the object to the center of the Earth.
1. A=ks² It begins with the area, A, which varies directly with the square of s, or s². Since no constant of variation was given we use k.
2. F=k/d² It begins with the force of gravity, or F, which is inversely proportional to the square of the distance to the center of the Earth, or d². Because it is inversely proportional, it is the denominator. No constant of variation is given so k is used.
Domain and Range
Continuous or noncontinuous
Bounded above, below ,or no bound
State all asymptotes
Domain: All reals
Range: All reals
Increasing for all x
No local extrema
No Horizontal Asymptotes
No Vertical asymptotes
End behavior: (-∞, ∞)
Continuous on [0,∞)
Increasing on [0,∞)
Bounded below but not above
Local minimum at x=0
No Horizontal asymptotes
No vertical asymptotes
End Behavior: [0,∞)
Demana, Franklin D. Precalculus: Graphical, Numerical, Algebraic. Boston: Addison-Wesley, 2007. Print.
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