## Explorations 64

MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

## Explorations 64. Group Activity Rational Powers Working in a group of three students, investigate the behavior of power functions of the form

f(x)=k \cdot x^{m / n}

, where

m

and

n

are positive with no factors in common. Have one group member investigate each of the following cases: -

n

is even -

n

is odd and

m

is even -

n

is odd and

m

is odd For each case, decide whether

f

is even,

f

is odd, or

f

is undefined for

x<0

. Solve graphically and confirm algebraically in a way to convince the rest of your group and your entire class. (1)

n

is even. For this case, decide whether

f

is even,

f

is odd, or

f

is undefined for

x<0

. Solve graphically and confirm algebraically in a way to convince the rest of your group and your entire class. (2)

n

is odd and

m

is even. For this case, decide whether

f

is even,

f

is odd, or

f

is undefined for

x<0

. Solve graphically and confirm algebraically in a way to convince the rest of your group and your entire class. (3)

n

is odd and

m

is odd. For this case, decide whether

f

is even,

f

is odd, or

f

is undefined for

x<0

. Solve graphically and confirm algebraically in a way to convince the rest of your group and your entire class.