Pre-Calculus Prep: VOLUME 1: FUNCTIONS

This video is a compilation going over the following topics…

Sure! Here's a brief description of each topic:

1. Continuity: In geometry, continuity refers to the property of a curve or function where there are no abrupt changes, breaks, or gaps. It means that the curve or function can be drawn or traced without lifting the pencil.

2. Extrema, Intervals of Increase and Decrease: Extrema are the maximum and minimum points of a curve or function. Intervals of increase and decrease refer to the portions of a curve or function where it is either getting larger (increasing) or getting smaller (decreasing).

3. Power Functions: Power functions are functions in the form f(x) = kx^n, where k is a constant and n is a real number. They are characterized by their shape and the rate at which they increase or decrease.

4. Average Rates of Change: In geometry, average rate of change measures the average speed at which a quantity changes over a specific interval. It calculates the ratio of the change in the quantity to the change in the independent variable.

5. Transformations of Graphs: Transformations of graphs involve changing the position, size, or shape of a geometric figure or function on a coordinate plane. Common transformations include translations, reflections, rotations, and dilations.

6. Piecewise Functions: Piecewise functions are functions that are defined by different equations or rules over specific intervals. Each interval has its own equation, and the function "switches" from one equation to another at specific points.

7. Operations: In geometry, operations refer to mathematical operations performed on geometric figures, such as addition, subtraction, multiplication, and division. These operations can involve lengths, areas, volumes, or other geometric properties.

8. Inverses: In geometry, inverses refer to the reverse or opposite of a geometric operation. For example, the inverse of a translation is the opposite translation in the opposite direction. Inverses help undo or reverse the effects of geometric transformations.

These topics form important components of geometry and provide the foundation for understanding various geometric concepts and solving geometric problems.

These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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