Precalculus I Lessons

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Functions

What is a Function?

Understand the definition of a function and how inputs map to outputs.

Domain and Range of Functions

Learn how to find the domain and range of any function, with clear examples.

The Graph of a Function

Explore how functions are visualized on a graph and what the graph tells us.

Increasing, Decreasing, and Constant Intervals

Learn how to analyze where functions are increasing, decreasing, or constant.

Even and Odd Functions

Discover what makes a function even, odd, or neither with symmetry examples.

Library of Parent Functions

Meet the most important basic functions that serve as templates for others.

Piecewise-Defined Functions

Understand how piecewise functions work and how to graph them correctly.

Graphing Techniques and Transformations

Function Transformations

Learn how to shift, stretch, reflect, and transform functions visually and algebraically.

Combining Functions (Add/Subtract)

Understand how to add and subtract functions and interpret the resulting graphs.

Combining Functions (Multiply/Divide)

See how multiplying or dividing functions affects their graphs and behavior.

Composition of Functions

Dive into composite functions and how to evaluate and decompose them effectively.

Equations, Lines, and Circles

Linear Equations | Slope, Graphing, and Line Equations Explained

Learn how to calculate and interpret slope, graph lines using a given point and slope, write equations in both point-slope and slope-intercept form, and find the equation of a line given two points.

Distance and Midpoint Formulas

Learn how to use the distance formula to calculate the distance between two points and how to use the midpoint formula to find the point halfway between two given coordinates.

Circles | Standard Form, Equations, Graphing

Learn how to interpret and write the standard form of a circle's equation, identify the center and radius, and graph circles step-by-step.

Quadratic Functions and Inequalities

Quadratic Equations

Walkthrough of quadratic equations that explains how to recognize them, solve them step-by-step, and understand what the solutions mean visually and algebraically.

Absolute Value Functions and Equations

Learn how to solve absolute value equations, identify when there are no solutions, graph absolute value functions with vertex shifts, and how to solve absolute value inequalities using compound statements.

Polynomials and Rational Functions

Asymptotes | Horizontal, Vertical, Oblique

Explanation of horizontal, vertical, and oblique asymptotes, showing how functions behave near them and how to identify each type from an equation or graph.

Exponential and Logarithmic Functions

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