SECTION 6.1SIMPLIFYING RATIONALEXPRESSIONS AND NPV’S
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REVIEW: WHAT IS A POLYNOMIAL FUNCTION?
A function that contains powers of “x” in the form of:
A,B,C,D,…E are Coefficients & must be real numbers
The exponents “n”, “n-1”…. have to be whole numbers
Can’t have “x” in the denominator or “x” as a radical
Ex#1) Indicate which of the following are not polynomials:
II) WHAT IS A RATIONAL FUNCTION?
A Rational Function is a function where you have onepolynomial function dividing another polynomialfunction.
EX#1) INDICATE WHICH OF THE FOLLOWING EXPRESSIONSARE RATIONAL FUNCTIONS:
III) SIMPLIFYING RATIONAL EXPRESSIONS
You can only simplify fractions when you have acommon factor in both the numerator & denominator
CommonFactor:
No CommonFactors
When Simplifying binomials, factor out the commonfactor first, then simplify
Factor
in thenumerator
Factor:in the numerator
IV) SIMPLIFYING R.E. WITH BINOMIALS
You can only cancel out a binomial only when it’s acommon factor in both the Numerator & Denominator
Can’t cancel, b/c thebinomials are not thesame
When there’s a trinomial or adifference of squares in theexpression, factor them first
Then cancel out any commonfactors or binomials in both thetop & bottom
Factor theexpression
Cancel out anycommon factors
PRACTICE: FACTOR AND SIMPLIFY
Factor theexpression
Cancel out anycommon factors
V) NON-PERMISSIBLE VALUES (NPV)
Permissible Allowed, Non Permissible Not Allowed
When evaluating rational expressions, the denominator isnot allowed to be Zero
Can’t divide by zero Undefined!!
Any value of “x” (variable) that makes the denominatorequal to zero is called a NPV
When finding the Non-Permissible Values
Take the entire denominator
Make it equal to zero
Then solve for “x” (variable)
Factor the denominator
These are values that “x” can not be (Not Permissible!)
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EX: FIND THE NPV FOR EACH EXPRESSION
Denominator
Equal to zero
Solve for “x”
“x” can NOT be 1/3,otherwise the expression will be undefined
Factor
For which value(s) of the variable is each expression undefined
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CHALLENGE: SIMPLIFY EACH EXPRESSIONAND FIND THE NPV
Denominator
NPV:
Can’t square root a neg. number
HW: SECTION 6.1
Assignment 6.1