 # Power Functions

Videos, worksheets, solutions, and activities to help PreCalculus students learn about power functions and variations.

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A power function is a function that can be written in the form
f(x) = kxa where a and k are non-zero contants. a is the power and k is the constant of variation or constant of proportion
The power function formulas with positive powers are statements of direct variation.
The power function formulas with negative powers are statements of inverse variation.
PreCalculus 2.2A Power Functions and Variation
Compare Monomials and Power Functions.

PreCalculus 2.2B Power Functions Variation
Joint Variation, Finding a power function from a table.
1) Charles' Law: The volume of an enclosed gas (at constant pressure) varies directly as the absolute temperature. If the pressure of 3.46L sample of neon gas at 302 degK is 0.926 atm, what would be the volume at a temperature of 338 degK, if the pressure does not change?
2) The weight that a board can support varies jointly with its width and the square of its thickness. A baord 8 feet long, 4 inches wide and 2 inches thick can support 200 pounds. How much weight could a board x feet long, 4 inches wide and 3 inches thick support?
A power function is a function where y = xn where n is a non-zero real constant number. Many of our parent functions such as linear functions and quadratic functions are in fact power functions. Other power functions include y = x3, y = 1/x and y = square root of x. Power functions are some of the most important functions in Algebra. All power functions pass through the point (1,1) on the coordinate plane.
Power Functions Degree End Behavior Even and Odd Functions
Write the equation of the power function p(x) that passes through a point.
A function is even if f(-x) = f(x)
A function is odd if f(x) = -f(x)

Integer Power Function.
Power functions are functions where y = xn where "n" is a non-zero real constant number. When "n" is a positive integer, we have two possible scenarios of an integer power function. When "n" is odd, the function passes through the origin, (1,1) and (-1,-1). Also, as the exponent increases, the function becomes steeper. When "n" is even, the function passes through the origin, (1,1) and (-1,1). These functions are symmetric about the origin.
How we identify odd power functions and even power functions.

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