Algebra II Chapter 8
Combined variation
When one quantity varies directly and/or inversely as two or more other quantities
From what the domain can't be
Where do you get the numbers for the Vertical Asymptote or hole
z=kx/wy
Write the combined variation for: z varies directly with x and inversely with the product wy
z=kxy
Write the combined variation for: z varies jointly with x and y
z=kxy/w
Write the combined variation for: z varies jointly with x and y and inversely with w
y=a/x-h +k
Write the inverse variation equation
Removable discontinuity
a characteristic of a function in which the function is continuous everywhere except for a hole -is a result of the denominator being canceled by part of the numerator
Rational function
a function whose rule can be written as a rational expression
Rational expression
a ratio of two polynomial expressions
Factor the polynomial then cross out like terms but don't forget limitations for the variables
How do you simplify a rational expression
Multiply by the least common denominator to get rid of all the fractions, don't forget limitations
How do you solve rational equations
Stretch, compress or reflect over x-axis
In the equation y=a/x-h +k what does a stand for
Horizontal translation and asymptote at x=h
In the equation y=a/x-h +k what does h stand for
Vertical translation and asymptote at y=k
In the equation y=a/x-h +k what does k stand for
Direct Variation
The relationship between two variable quantities that have a constant ratio. y=kx
Find a common denominator or multiply by common denominator
What are the two ways to add and subtract rational expressions
y/x
What is k in direct variation
xy
What is k in indirect variation
y=coefficient of highest degree term in the numerator/coefficient of highest degree term in the denominator
What is the horizontal asymptote if the degree of the numerator is equal to the degree of the denominator
No HA
What is the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator
y=0
What is the horizontal asymptote if the degree of the numerator is smaller than the degree of the denominator
Use hole when the denominator is canceled by part of the numerator and use vertical asymptote all other times
When do you use vertical asymptote vs hole
Inverse variation
an equation of the form y = k/x, where k is not equal to zero
Rational equation
an equation that contains one or more rational expressions -When solving these make sure to check for extraneous solutions
Nonremovable discontinuity
describes infinite and jump discontinuities because they cannot be eliminated by redefining the function at that point -Vertical asymptote
Constant of variation
the constant k in direct and inverse variation equations
