Midterm Study Guide Flashcards
Natural/counting numbers
All positive integers {1, 2, 3, 4, 5, 6…}
Whole numbers
Including 0 with all positive integers: {0, 1, 2, 3…}
Rational numbers
A number expressed as the quotient of two integers (p/q)
Irrational numbers
Decimals that don’t have a pattern (like pi)
Real numbers
Rational+irrational numbers (not complex)
Percent increase formula
Amount of increase/original amount
Percent decrease formula
Amount of decrease/original amount
|ax+b|= k
ax+b=k or ax+b=-k
“Or”=
Union
“And”=
Intersection
|ax+b|>k
ax+b>k or ax+b<-k
|ax+b|< k
-k<ax+b<k
Midpoint formula
M = ((x1+x2)/2, (y1+y2)/2)
Slope formula
m=rise/run= (y2-y1)/(x2-x1)
Horizontal line equation and slope
y=b, m=0
Vertical line equation and slope
x=a, undefined slope
Slope of parallel lines
Same slope
Slope of perpendicular lines
-1/m
Point-slope form
y-y1 = m(x-x1)
Relations
Any set of ordered pairs
Functions
For each distinct x-value, there is exactly one y-value
Domain
x-values
Range
y-values
Vertical line test
If every vertical line intersects the graph of a relation in no more than one point, then the relation is a function
Function notation
y=f(x)
Linear functions
f(x) = ax+b
Polynomials
A polynomial is a term or a finite sum of terms of the form ax^n
Numerical coefficient
In a term ax^n, a is the coefficient
Degree of the term
In ax^n, n is the degree of the term
Polynomials are written in…
Descending powers. The greatest-degree term is the leading term and its coefficient is the leading coefficient. The degree of a polynomial is the greatest degree of all its terms (if there is only one variable)
