Power Functions with Modeling power function: a function of the form Note: k and a can be any non-zero real number power: the number a constant of variation: the number k polynomial function: a power function where the exponent is a non-negative integer (zero?) NOTE: monomials are ONE term polynomials

Ex 1: Determine whether the function is a power function. If so, state its power and constant of variation. Assume c, g, and k are constants. yes; 2; 3 yes; 1; c 2 no yes; 2;

Ex 2: Determine whether the function is a monomial function. If so, state its degree and coefficient. If not, state why not. yes; 2; 3 yes; 0; 12 no; x is the exponent no; negative exponent no; can’t have two terms

What five of the 12 Basic Functions are Power Functions??? In other words: What five of the 12 Basic Functions have nonzero real numbers as exponents???

Power Functions with Modeling direct variation: when k is multiplied by the variable inverse variation: when k is divided by the variable joint variation: when k is multiplied by multiple variables

Ex 3: Writing power functions from word problems. The period of time T for the full swing of a pendulum varies directly as the square root of the pendulum’s length, l. Express this as a power function. Since this is a direct variation, and we were not given a different constant of variation, we will have k times the variable with its power.

Ex 4: Writing power functions from word problems. The current I in an electrical circuit is inversely proportional to the resistance R, with constant of variation V. Since this is an inverse variation, the constant of variation is divided by the variable and its power.

Ex 5: Writing word problems from power functions. Express the relationship, where V is the volume, r is the radius and h is the height of a cylinder using the language of variation. Since there is no division this is a direct variation, and since there are multiple variables it is a joint variation. The volume V of a cylinder varies jointly with the radius r of the cylinder squared and the height h of the cylinder, with constant of variation π.

Power Functions HW Assignment Power Functions Worksheet (1-20 all) ***Bonus (21-25 all)***