Distance and Midpoint Between Points

• Distance Formula: The distance between two points and is given by:

• Midpoint Formula: The midpoint between two points and is:

• Example: Find the distance and midpoint between and .

Slope and Intercept of a Line

• Slope Formula: Point-Slope Form:

• Slope-Intercept Form:

• Example: Find the equation of a line passing through with slope 4.

Linear Equations, Composition of Functions

• Linear Equation: Composition of Functions:

• Example: If and , find .

Quadratic Functions & Equations; Inequalities

• Standard Form: Quadratic Formula:

Inequalities

Solving inequalities involves finding the set of values that satisfy a given condition.

• Linear Inequality: Quadratic Inequality:

• Example: Solve .

Polynomial Functions & Rational Functions: Domain & Range

Understanding the domain and range is essential for analyzing functions.

• Domain: The set of all possible input values () for which the function is defined.

• Range: The set of all possible output values ().

• Rational Function: , where .

• Finding Asymptotes: Vertical asymptotes occur where ;

• horizontal asymptotes depend on the degrees of and .

• Example: Find the domain and asymptotes of .

Exponential Functions & Logarithmic Functions Inverse Functions; Exponential & Log Equations

• Exponential Function: Logarithmic Function:

• Inverse Function: If and are inverses, and .

• Example: Find the inverse of .

Properties and Applications of Logarithms

Product Rule: Quotient Rule:

Power Rule: Example: Expand .

Solving Systems of Equations

• System of Two Equations: System of Three Equations:

• Methods: Substitution, elimination, and matrix methods (such as Gaussian elimination).

• Example: Solve

  Exponential Growth and Decay Applications to Half-Life and Growth Problems

• Exponential Growth: Exponential Decay:

• Half-Life Formula: