Flashcards for Blake

Natural, Whole, Integers, Rational, Irrational, Real

Subsets of the real number system

a(b+c) = ab + ac

Distributive property

A number that doesn’t change the value (0 for addition, 1 for multiplication)

Identity element

All elements from both sets

Union ( ∪ )

Only elements common to both sets

Intersection ( ∩ )

Distance of a from 0 on the number line

|a|

a^(m+n)

Exponent rule: a^m · a^n

a^(m-n)

Exponent rule: a^m / a^n

Writing a number as a × 10^n, where 1 ≤ |a| < 10

Scientific notation

The highest exponent of the variable

Degree of a polynomial

The coefficient of the highest-degree term

Leading coefficient

a^2 - b^2

Special product: (a+b)(a-b)

Writing a polynomial as a product of simpler polynomials

Factoring

(x-3)(x+3) (difference of squares)

Factor x^2 - 9

All real numbers except those making the denominator 0

Domain of a rational expression

A fraction with another fraction in numerator and/or denominator

Complex fraction

x = (-b ± √(b^2 - 4ac)) / 2a

Quadratic formula

Tells type of roots (real/imaginary, distinct/repeated)

Discriminant (b^2 - 4ac)

Solve ax+b=c and ax+b=-c

Solve |ax+b| = c

An inequality involving distance from zero, like |x| < a

Absolute value inequality

d = √((x2-x1)^2 + (y2-y1)^2)

Distance formula

M = ((x1+x2)/2, (y1+y2)/2)

Midpoint formula

a^2 + b^2 = c^2

Pythagorean theorem

m = (y2-y1)/(x2-x1)

Slope formula

y-y1 = m(x-x1)

Equation of a line (point-slope form)

Parallel: equal slopes; Perpendicular: slopes are negative reciprocals

Parallel vs perpendicular slopes

Ax+By=C, A,B,C integers

Standard form of a line

The point(s) where a graph crosses the x-axis (y=0)

x-intercept

The point where a graph crosses the y-axis (x=0)

y-intercept

The line rises from left to right

Positive slope

The line falls from left to right

Negative slope

m=0

Slope of a horizontal line

Undefined

Slope of a vertical line

y = mx + b

Slope-intercept form of a line

y-y1 = m(x-x1)

Point-slope form of a line

Ax+By=C

Standard form of a line

The set of all possible input values (x-values)

Domain of a relation

The set of all possible output values (y-values)

Range of a relation

A graph represents a function if no vertical line intersects it more than once

Vertical line test

Where the graph goes up (as x increases, y increases)

Increasing interval

Where the graph goes down (as x increases, y decreases)

Decreasing interval

Adding/subtracting a constant outside the function, f(x)+k

Vertical shift

Adding/subtracting inside the function, f(x-h)

Horizontal shift

Multiply the function by -1: -f(x)

Reflection across the x-axis

Replace x with -x: f(-x)

Reflection across the y-axis

Multiply f(x) by a constant a: if |a|>1, stretch; if 0<|a|<1, compression

Vertical stretch/compression