Chapter 9 (Alg 2)

Question 1

Inverse variation

Answer 1

y = k over x where k DNE 0

the variable y is said to vary inversely with x

Question 2

Constant of variation

Answer 2

k, the nonzero constant

Question 3

Joint variation

Answer 3

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

Question 4

Types of variation

Answer 4

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

Question 5

Rational Function

Answer 5

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

Question 6

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

Answer 6

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

Question 7

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

Answer 7

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

Question 8

Graphs of General Rational Functions

Answer 8

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)

Question 9

Rational Expression

Answer 9

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

Question 10

Simplyfying Rational Expressions

Answer 10

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

Question 11

multiplying Rational Expressions

Answer 11

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

Question 12

Dividing rational Expressions

Answer 12

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

Question 13

Complex fraction

Answer 13

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

Question 14

Adding and Subtracting Rational Expressions

Answer 14

fractions with same denominator you can subtract the rational expressions

Question 15

Least Common Denominator, LCD

Answer 15

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.

Question 16

Rational equation

Answer 16

an equation that contains rational expressions

Question 17

Cross multiply

Answer 17

when each side of the equation is a single rational expression