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
