Unit 8 Flashcards
Rational Expression
Ratio of two polynomial expressions
Steps to Simplify a Rational Equation
- Factor everything that can be
- Simplify the monomials using exponent rules
- Eliminate common binomial factors
Dividing Rational Expressions
Multiply by the recipricol
Steps to Simplify Complex Fractions With Multiple Denominator Fractions
- Find LCD
- Multiply each term by LCD/1 to clear fractions
- Simplify if possible
Variation
A special relationship between variables
Variation Models
Direct variation
Joint variation
Inverse variation
Direct Variation
y=kx
y is directly proportional to x
Joint Variation
y=kxz
y varies jointly as x and z
Inverse Variation
y=k/z
y is inversely proportional to x
Constant of Variation
k
Combined Variation
A relationship that contains both direct and inverse variation
Excluded Values
Values that make denominator of rational expressions equal to zero or undefined
Always Remember To
Check your solution
h
Is the horizontal shift
Positive shifts right
Negative shifts left
k
Is the vertical shift
Positive shifts up
Negative shifts down
|a|>1
Represents a vertical stretch
0<|a|<1
Represents a vertical compression
Positive a
Hyperbola in quadrant I and III
Negative a
Hyperbola in quadrant II and IV
Rational Functions
A function of the form f(x)=p(x)/q(x)
p(x) and q(x) are
Polynomials such that q(x)≠0
Top>Bottom
No H.A.
Top<Bottom
y=0
Top=Bottom
Divide the leading co-efficient
Hole
A point at which there is a break in the graph
Hole Occurs When
There is common factor between the numerator and denominator
ALWAYS CHECK FOR MORE SIMPLIFYING
GCF
DIFFERENCE OF SQUARES
PLEASEEE
REMEMBER
When there is addition/subtraction, you can’t cross cancel
PLEASE
LOOK FOR GCF
CHECK ANSWERS
K STAYS NOT X
SOLVE TO MAKE VARIATION CORRECT
