Section 1
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Cards (138)
Section 1
(50 cards)
Domain
Set of all input values.
Piecewise Functions
A function that is defined by more than one function.
>
Greater Than
Standard Form of Linear Equations
A linear equation in the form 'Ax+By=C.'
Relation
A mapping, or pairing, of input values with output values.
Constant
A non-varying value.
Parabola
Absolute Value
The distance a number is from 0 on a number line. (Can never be negative.)
Function Notation
y=f(x), the value of the function when x is a certain value.
Absolute Value Graphs
Term
A component of a logical or mathematical expression.
P.E.M.D.A.S
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Celcius to Fahrenheit Conversion Formula
F=(9/5)C+32 -F=degrees (fahrenheit) -C=degrees (celsius)
Conjugate
Used to rationalize the denominator of a fraction.
Elimination
Properties of 'i'
-'i'='i' -'i^2'=-1 -'i^3'='-i' -'i^4'=1 -'i^5'='i' -'i^6'=-1 -'i^15'=-1 -'i^34'=-1
Imaginary Numbers
A complex number that can be written as a real number multiplied by the imaginary unit 'i.'
Principal Square Root
The positive square root.
Simple Interest Formula
I=Prt -P=principal (original amount of money) -r=interest rate (written as a decimal) -t=time (years)
Pythagorean Theorem of Baseball
W/T≈R^2/R^2+A^2 -W=wins -T=games played -R=runs scored -A=runs allowed
Rate of Change
Slope that represents how much one quantity changes on average, relative to the change in another quantity.
Parallel Lines
Lines are parallel if and only if they have the same slope.
Square Root
A number, 'r,' is a square root of a number, 's,' if r^2=s. -3^2=9 and (-3)^2=9 so 3 and -3 are square roots of 9
Substitution
Coefficient
A multiplicative factor in some term of a polynomial, a series, or any expression.
Radical
Operator to the square root.
GCF
Greatest Common Factor
Slope-Intercept Form
y=mx+b -m=slope -b=y-intercept
Zeroes
Solutions (also see 'Root / X-Intercept / Zero')
Complex Numbers
A number that can be expressed in the form 'a+bi,' where 'a' and 'b' are real numbers and 'i' is the imaginary unit, that satisfies the equation i^2=-1.
General Equation of an Absolute Value Function
y=a|x-h|+k -a=rate of change -(h,k)=vertex
Perpendicular Lines
Lines are perpendicular if and only if they have negative reciprocal slopes.
Properties of Quadratics in Standard Form
-The vertex is (-b/2a , f(-b/2a)) -The axis of symmetry is x=-b/2a -The y-intercept is C -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent
Vertical Line Test
A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.
Point-Slope Form
y − y1 = m(x − x1). -m=slope -(x1,y1)=a given point
Variable
A symbol that represents a quantity in a mathematical expression, as used in many sciences.
Range
Set of all output values.
Function
A relation for which each input has exactly one output.
Radicand
Expression under the radical.
Standard Form of Quadratic Functions
y=ax^2 +bx+c -a≠0
Parent Function
The most basic function in a family.
Completing the Square
Slope
Denoted by 'm,' of a non-vertical line is the ratio of the vertical change to the horizontal change.
Vertex Form of Quadratic Functions
y=a(x-h)^2 +k -a≠0 -the graph is a parabola -Parent Function is f(x)=x^2
Difference of Squares
LCM
Least Common Multiple
Properties of Quadratics in Vertex Form
-The vertex is (h,k) -The axis of symmetry is x=h -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent
<
Less Than
Zero Product Property
If AB=0, then A=0 or B=0.
Expression
A finite combination of symbols that are well-formed according to applicable rules.
Section 2
(50 cards)
Logarithm
The inverse operation to exponentiation. y = log(b) x if and only if b^y = x -b > 0 -b ≠ 1 -x > 0
Root / X-Intercept / Zero
Where a function crosses the x-axis.
Polynomial Function
f(x)=ax^n +bx^n-1 +cx^n-2+...+dx+e -a=leading coefficient -n=degree
Polynomial Graphs
Synthetic Division
Power Function
y=ax^b, where 'a' is a real number and b is a rational number.
Radical Form to Rational Exponent Conversion
∜81=81^¼ Even Roots: -a < 0: no real nth roots -a = 0: one real nth root (0) -a > 0: two real nth roots Odd Roots: one real nth root
Factoring with Cube Patterns
Properties of Logarithms
-log(b) xy = log(b) x + log(b) y -log(b) x/y = log(b) x - log(b) y -log(b) x^y = ylog(b) x
Exponential Decay Function
An exponential function that 'decays' towards the asymptote as you move left to right. -0 < b < 1
Horizontal Line Test
The inverse of a function 'f' is also a function if and only if no horizontal line intersects the graph of 'f' more than once.
Finding Horizontal Asymptotes of a Rational Function
-If power on bottom is bigger, then set 'y' equal to zero -If power on top is bigger, there is no asymptote -If powers are the same, then asymptote is coefficients
Vertical Motion Quadratic Function
h(t)=-16t^2+vt+s -h=height of object (feet) -t=time (seconds) -v=initial velocity of object (ft/sec) -s=initial height of object (feet)
Product Property of Radicals
√ab = √a * √b
Change-Of-Base Formula
log(c) a = (log a) / (log c)
Synthetic Substitution
Quotient Property of Radicals
√(a/b) = (√a) / (√b)
Factoring by Grouping
The process of factoring four terms by grouping them in pairs, factoring the GCF from each pair, and looking for a common binomial factor.
e
The base of the natural logarithm. Approximately equal to 2.718281828459, it is the figurative asymptote of the function (1+1/n)^n.
Extrema
The collection of the largest and smallest values of a function.
Rational Functions
y=(a/(x-h)) + k, a polynomial divided by a polynomial.
Absolute (Global) Extrema
The collection of the largest and smallest values on the entire domain of a function.
Percent Decrease Model
y=a(1 - r)^t -a=initial value -r=% increase (or decrease) -t=time
Common Logarithm
log(10) x written as log x
Exponential Growth Function
An exponential function that 'grows' away from the asymptote as you move left to right. -b > 1
Two-Step Factoring
First, factor out any GCF from the original problem, then factor normally.
Exponential Function
y=a(b)^x, a function in which the variable is in the exponent. -a=initial value -b=growth/decay factor
Discriminant
A function of a polynomial's coefficients, giving information about the nature of its roots. -If b^2-4ac > 0, the (2) roots are positive -If b^2-4ac < 0, the roots are negative and imaginary -If b^2-4ac = 0, the (1) root equals zero
Exponent Rules
-a^m * a^n = a^m+n -a^m / a^n = a^m-n. (a≠0) -(a^m)^n = a^mn -(ab)^n = a^n * b^n -(a/b)^n = a^n / b^n -a^-n = 1/a^n -a^0 = 1. (a≠0)
Simplest Form of Radicals
No perfect nth powers as factors and any denominator has been rationalized.
Rational Exponent Rules
-a^m * a^n = a^m+n -(a^m)^n = a^mn -(ab)^m = a^m * b^m -a^-m = 1/a^m -a^m / a^n = a^m-n. -(a/b)^m = a^m / b^m -ax^m ± bx^m = (a ± b)x^m
Natural Logarithm
log(e) x written as ln x
Finding Vertical Asymptotes of a Rational Function
Set denominator equal to zero.
Inverse Relation
An interchange of the input and output values of the original relation.
Relative (Local) Extrema
The collection of the largest and smallest values of a function within a given range.
Properties of Equality
-b^x = b^y if and only if x=y -log(b) x = log(b) y if and only if x=y (b > 0, b ≠ 1)
Square Root Function
f(x) = √x
Logarithmic Functions
Periodic Compounding Interest Formula
A=P(1+r/n)^nt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal) -n=number of times the interest is compounded (paid) per year
Quadratic Formula
Asymptote
An imaginary line that a graph approaches more and more closely.
Percent Increase Model
y=a(1 + r)^t -a=initial value -r=% increase (or decrease) -t=time
Inverse Function
When both the original relation and the inverse relation are functions. -Written as f^-1(x) ✩ NOT A NEGATIVE EXPONENT!
Composition of a Function
h(x)=g(f(x)), the pointwise application of one function to the result of another to produce a third function.
Polynomial Long Division
Finding X-Intercepts
Find 'x' when y=0
Cubic Root Function
f(x) = a(∛(x-h)) + k a: -if |a|gets bigger, then there is a vertical stretch -if |a| gets smaller, then there is a vertical shrink -if a is negative, then the graph flips h: -translates graph 'h' units horizontally k: -translates graph 'k' units vertically
End Behavior
The behavior of the graph of f(x) as 'x' approaches positive infinity or negative infinity.
Factoring Polynomials in Quadratic Form
It is sometimes necessary to factor out any factor that might be common to all terms first. The two terms in 5x^2 - 10, for example, both contain the factor '5'. This means that the expression can be rewritten as 5(x^2 - 2).
Continous Combounding Interest Formula
A=Pe^rt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal)
Section 3
(38 cards)