Section+2.2

Power Functions with Modeling Power Function: f(x)= KX^a; where "a" is power & "k" is constant of variation f(x) varies as the ath power of x; f(x) is proportional to ath power of x f(x)=KX^a direct variation f(x)=K/X^a inverse  variation Ex. C of circle varies directly as its radius C=2(pie)r power=1 constant=2pie Ex. A=(pie)r^2 power=2 Area of the circle varies directly as the square of the radius Constant=pie Ex. Volume of enclosed gas is inversely proportional to the applied pressure V=k/p power=-1 constant=K Ex. Period of time, t, for full swing of pendulum varies as square root of pendulum's length, l. T=K(square root of L) power= 1/2 constant=K Ex. State power & constant f(x)= (cube root) X g(x)= 1/x^2 power=1/3 power=-2 constant=1 constant=1

End Behavior: what are the y-values of graph doing as x goes to (+) or (-) infinity || Positive || Negative || ||  parabola with both arrows up  ||  parabola with both arrows down || ||  up right; down left || up left; down right ||
 * Constant/ power
 * even
 * odd

Negative power: ends go towards the x-axis Ex. Find values of K and a. Determine any symmetry(even, odd, undefined for x<0) f(x)=2x^-3 f(x)= -.4x^1.5 a=-3 odd a=1.5 undefined for x<0 K=2 K=-.4 f(x)=-x^.4= -x^2/5= -(5th root of x) squared; even symmetry Power functions graphically: All power functions go through (1, k) If k<0, reflects over x-axis Homework: Pg. 196, #1-35 odd; #55