Limits

Integers

all whole numbers positive and negative ℤ

real numbers

all numbers that can be placed on a number line ℝ

Ways to express a function

Algebraically

Geometrically

Numerically

What makes a function a function?

• algebraically: 1 input for each output

• Geometrically: Vertical line test

Piece wise function

functions that are defined by using different rules for different parts of the domain.

Toolbox for functions

Constant: f(x) = c

Linear: f(x)= mx + b

Quadratic: f(x)= ax² + bx + c

Polynomials: P(x)= a​​_nxⁿ + a​​_n-1x^n-1 + …….+ a​​₁x + a_{0 (although all the above equations also constitute as polynomials.}

criteria for polynomial functions

Polynomials are a finite sum of terms axⁿ where….

• a is a real number

• n is a non-negative integer (remember square roots are still fractional exponents.

• The domain is always all real numbers

Geometric approach to limits