Section 2-2 Power Functions

Section 2-2 power functions power functions variation variation some common power functions some common power functions graphs of power functions graphs of power functions modeling with power functions modeling with power functions

Power Functions power functions can be written in the form: power functions can be written in the form: a is the power and k is the constant of variation a is the power and k is the constant of variation many common formulas found in geometry and science are power functions many common formulas found in geometry and science are power functions

Variation power functions with positive powers are called direct variation power functions with positive powers are called direct variation power functions with negative powers are called inverse variation power functions with negative powers are called inverse variation unless the word inversely is included in a variation statement it is assumed to be direct unless the word inversely is included in a variation statement it is assumed to be direct

Common Power Functions identity:square root: cubing: reciprocal: squaring:cube root: inverse-square:

Graphing Power Functions to graph power functions in the form to graph power functions in the form consider what they would look like in quadrant I (without k) consider what they would look like in quadrant I (without k) if k < 0 then the graph will be in the quadrant IV instead of the quadrant I if k < 0 then the graph will be in the quadrant IV instead of the quadrant I

Power Functions in Quad I

Graphing Power Functions One of three things happens when x < 0 f is undefined for x < 0 (no more graph) f is undefined for x < 0 (no more graph) f is even, so the rest of the graph is symmetric about the y-axis f is even, so the rest of the graph is symmetric about the y-axis f is odd, so the rest of the graph is symmetric about the origin f is odd, so the rest of the graph is symmetric about the origin see example #4 on page 185 see example #4 on page 185

Modeling With Power Functions enter data into the calculator lists enter data into the calculator lists data should include (0, 0) or it should not have a different y-int data should include (0, 0) or it should not have a different y-int go to STAT CALC and find PWRREG for power regression go to STAT CALC and find PWRREG for power regression use the equation to answer other questions and make predictions use the equation to answer other questions and make predictions