# Combination of Function: Evaluation of Division

Example:

Evaluate when and

Solution:

 Evaluate the function Rewrite the expression Replace x with -3 in each function Simplify Division by zero is undefined is undefined

is undefined.

# Composition of Functions

Example:

Find when

and

Solution:

 The definition of composition Replace each x in f with g(x) Simplify and write a single fraction by finding a common denominator Simplify by using the distributive property and combine like terms.

# Using the Min and Max Feature in the Calculator

Example:  Find the difference quotient for

The Difference Quotient:

Solution:

 The Difference Quotient Formula Write the difference quotient for the given function = Apply the exponent and use the distributive property = Multiply = Combine the like terms = Combine the like terms.  Only terms with h should remain = Divide h into each term = Cancel the common h from each term =

# Difference Quotient: Rational Function

Example:  Find the difference quotient for

The Difference Quotient:

Solution:

 The Difference Quotient Formula Write the difference quotient for the given function = Use the distributive property = Simplify the complex fraction by multiplying the numerator and denominator by the common denominator = Distribute the common denominator to each fraction in the numerator. = Cancel the common factor = Multiply the expression in the numerator = Combine like terms = Cancel a common h from the numerator and denominator =

# Difference Quotient: Rational Function

Example:  Find the difference quotient for

The Difference Quotient:

Solution:

 The Difference Quotient Formula Write the difference quotient for the given function = Simplify the complex fraction by multiplying the numerator and denominator by the common denominator = Distribute the common denominator to each fraction in the numerator. == Cancel the common factor == Simplify by squaring the binomial === Simplify by combining like terms and distributing the negative == Combine like terms = Cancel a common h from the numerator and denominator =

The difference quotient for is