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