Mathematical Models Flashcards
Axioms
Mathematical statements that serve as starting points for other statements and are logically derived.
Tou can’t prove something using nothing
Axioms are unproved truths 1+1=2
Continuous Quantitative Variables
infinite number of values between 2 values (i.e. decimal points)
Discrete Quantitative Variables
a finite number of values between 2 values (i.e. no decimal points)
Functions
You put X into a given function and get Y out of it.
A weekly salary (X) is a function of the Hourly Pay and number of Hours Worked.
HP x HW = X(the function)
X and Y are the axis of th graph and the function is the plotted point
ex.
f(x) = a². also means y = a²
Theorem
Statements logically derived from or proven by one or more axioms or previous statements.
Linear Equations
f(x) = ax + b
Quadratic Equation
f(x) = ax² + bx + c
Exponential Equation
f(x) = a^{x}
Logistic Equation
f(x) = a ÷ (c + b^{x})
Logarithmic Equation
f(x) = log,{a}(x)
Trigonomic Equation
f(x) = cos(x) f(x) = sin(x)
Polynomial Equation
ax + bx² + cx³
Vertical Shift
f(x)±b
If b is positive+ it moves up
If b is negarive- it moves down
Horizontal Shift
f(x±c)
If C is positive+ it moves left
If C is negative- it moves right
Vertical Stretch/Squeeze
d*f(x)
If d is more than 1 or less than -1 it STRETCHES
If d is a decimal it SQUEEZES
