Section 2-1: Power and Radical
Functions

A power function is any function of the
form f(x) = axn where a and n are
nonzero constant real numbers.
◦ A monomial function can be written
f(x) = a or f(x) = axn .
Section 2-1: Power and Radical
Functions

Monomial functions
Section 2-1: Power and Radical
Functions

Monomial functions
Section 2-1: Power and Radical
Functions

Example:
Section 2-1: Power and Radical
Functions

Example (monomial functions):
◦ Graph
◦ Analyze
◦ Domain
◦ Range
◦ Intercepts
◦ End behavior
◦ Continuity
◦ Increasing
◦ Decreasing
Section 2-1: Power and Radical
Functions

Example (fxns w/negative exponents):
◦ Graph
◦ Analyze
◦ Domain
◦ Range
◦ Intercepts
◦ End behavior
◦ Continuity
◦ Increasing
◦ Decreasing
Section 2-1: Power and Radical
Functions

Example (fxns w/negative exponents):
◦ Graph
◦ Analyze
◦ Domain
◦ Range
◦ Intercepts
◦ End behavior
◦ Continuity
◦ Increasing
◦ Decreasing
Section 2-1: Power and Radical
Functions

Example (rational exponents):
◦ Graph
◦ Analyze
◦ Domain
◦ Range
◦ Intercepts
◦ End behavior
◦ Continuity
◦ Increasing
◦ Decreasing
Section 2-1: Power and Radical
Functions

A radical function is a function that can
be written as
where n and p are positive integers
greater than 1 that have no common
factors.
Section 2-1: Power and Radical
Functions
Section 2-1: Power and Radical
Functions

Example (radical functions):
◦ Graph
◦ Analyze
◦ Domain
◦ Range
◦ Intercepts
◦ End behavior
◦ Continuity
◦ Increasing
◦ Decreasing
Section 2-1: Power and Radical
Functions

Raising each side of an equation to a
power sometimes provides extraneous
solutions, or solutions that do not
satisfy the original equation.
◦ Always check your work!
Section 2-1: Power and Radical
Functions

Example (solving radical equations):
Solve
Section 2-1: Power and Radical
Functions

Homework:
Pages 92-93
#3, 6, 9, 18, 21, 37, 47, 50
◦ Due Thursday for grading: #12 & #48