# Chapter 9 (Alg 2) Flashcards

1
Q

Inverse variation

A

y = k over x where k DNE 0

the variable y is said to vary inversely with x

2
Q

Constant of variation

A

k, the nonzero constant

3
Q

Joint variation

A

when a quantity varies directly as the product of two or more other quantities

4
Q

Types of variation

A
```y = kx; y varies directly with x
y = k / x; y varies inversely with x
z = kxy; z varies directly with x,y
y = k / x^2; y varies inversely with the square of x
z = ky / x; z varies with y and inversely with x```
5
Q

Rational Function

A

a function in the form of f(x) = p(x) / q(x) where p(x) and q(x) are polynomials and q(x) DNE 0
{}
each graph is a hyperbola
x-axis is a horizontal asymptote and the y-axis is a vertical asymptote
graph has two symmetrical parts called branches
for each point (x,y) on one branch of y = 1/x, the corresponding point (-x,-y) is on the other branch

6
Q

Deatails about the functions in the form of y = a/x

A

If a > 0, the branches of the hyperbola are in the first and third quadrants
If a

7
Q

Graphing Rational Functions of the Form y = a over x-h + k

A

vertical asymptote at x = h and a horizontal asymptote at y = k

8
Q

Graphs of General Rational Functions

A
```let p(x) and q(x) be polynomials with no common factors other than + or - 1. The graph of the rational function f(x) = p(x) over q(x) has the following characteristics:
x intercepts of the graph of f(x) are the real zeros of p(x)
the graph of f(x) has a vertical asymptote at each real zero of q(x)```
9
Q

Rational Expression

A

a fraction whose numerator and denominator are non zero polynomials is a rational expression

10
Q

Simplyfying Rational Expressions

A

let a, b, and c be nonzero real numbers or variable expressions
ac / cb = ac / bc = a / b

11
Q

multiplying Rational Expressions

A

let a, b and c be nonzero variable expressions
to multiply, multiply numerators and denominators
a / b * c / d = ac / bd

12
Q

Dividing rational Expressions

A

let a, b, c and d be nonzero variable expression. Use these steps to find the quotient
a / b / c / d = a /b * d /c

13
Q

Complex fraction

A

(a / b) / (c / d) = a / b * d / c

14
Q

Adding and Subtracting Rational Expressions

A

fractions with same denominator you can subtract the rational expressions

15
Q

Least Common Denominator, LCD

A

the least common denominator can be found by using the least common multiple of the denominators
{}
another way to solve a rational equation is to multiply each term on each side of the equation by the least common denominator (LCD) of the terms.

16
Q

Rational equation

A

an equation that contains rational expressions

17
Q

Cross multiply

A

when each side of the equation is a single rational expression