Power Functions Power Functions Power functions are seen

Power Functions

Power Functions Power functions are seen when dealing with areas and volumes. volume of a sphere: Power functions also appear in gravitation.

Power Function Notation where k and p are constants k is referred to as the constant of proportionality

Direct Proportions The variable y is directly proportional to x when: y = k * x, where k is some constant value Alternatively, . As x increases, y must also increase to keep the value for k the same.

Direct Proportions EXAMPLE The more hours you work, the more money you earn. Amount earned is directly proportional to the number of hours worked.

Direct Proportions Suppose the constant of proportionality is 4 • As x goes up, y must go up. • So the slope is positive. • Then y = 4*x What does the graph of this function look like?

Inverse Proportions The variable y is inversely proportional to x when this is still a power function Alternatively, y = k * x -1 As x increases, y must decrease to keep the value for k the same.

Inverse Proportions EXAMPLE If you drive at a higher speed, it will take less time to arrive at your destination. Speed is inversely proportional to time.

Inverse Proportions Consider what the graph looks like… as x increases, y decreases

Power Functions Recalling our knowledge of transformations, what effect will k have? vertical stretch or compression

Special Power Functions • Parabola y = x 2 • Cubic Function y = x 3

Special Power Functions Most power functions are similar to one of the following: • xp with even powers of p are similar to x 2 • xp with negative odd powers of p are similar to x -1 • xp with negative even powers of p are similar to x -2