# Chapter 9 (Alg 2) Flashcards

Inverse variation

y = k over x where k DNE 0

the variable y is said to vary inversely with x

Constant of variation

k, the nonzero constant

Joint variation

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

Types of variation

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

Rational Function

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

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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

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

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

If a

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

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

Graphs of General Rational Functions

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)

Rational Expression

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

Simplyfying Rational Expressions

let a, b, and c be nonzero real numbers or variable expressions

ac / cb = a*c / b*c = a / b

multiplying Rational Expressions

let a, b and c be nonzero variable expressions

to multiply, multiply numerators and denominators

a / b * c / d = ac / bd

Dividing rational Expressions

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

Complex fraction

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

Adding and Subtracting Rational Expressions

fractions with same denominator you can subtract the rational expressions

Least Common Denominator, LCD

the least common denominator can be found by using the least common multiple of the denominators

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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.