Pre-Calculus Video Series

Explore exponent properties, including the product and power rules, negative exponents, and fractional exponents, through explicit examples and step-by-step simplification.

Explore the composition of functions by evaluating f(g(x)) and g(f(x)) from inside out, with concrete examples and results f(g(x))=4x^2+19 and g(f(x))=16x^2-8x+6.

Explores transformations of functions, including translations (left-right and up-down), dilations (vertical and horizontal), and reflections, with practical examples using linear, quadratic, absolute value, and exponential functions.

Sketch functions by transforming parent graphs, applying horizontal and vertical shifts, reflections, stretches, and compressions, and determine zeros, domain, range, and symmetry for polynomials, reciprocals, exponentials, absolutes, logs, and roots.

Analyze and graph piecewise functions by domain rules, ensuring non overlapping pieces and a valid vertical line test. Practice evaluating pieces and plotting with open and closed endpoints.

Explore graphing polynomial functions by identifying degree and leading coefficient, and analyzing end behavior. Locate zeros with multiplicities and sketch from factored form.

Explore dividing polynomials using exponent rules and coefficients, compute remainders and quotients with polynomial long division and synthetic division, and apply the factor theorem to factor polynomials.

Learn to factor polynomials using the rational root theorem, identify P and Q factors, test rational roots with synthetic division, and factor by grouping, including quadratics and difference-of-squares.

Learn to find complex zeros of polynomials by factoring to quadratics, using rational root theorem, quadratic formula, and square-root methods, and note that complex roots come in conjugate pairs.

Explore rational functions built from polynomials, including reciprocal forms, and learn to analyze asymptotes, intercepts, holes, domains, ranges, and graph transformations.

Solve non-linear inequalities using polynomials and rational functions, including factoring, zeros, and vertical asymptotes. Graph intervals on a number line, test points, and apply end behavior for sign analysis.

Explore function modeling to optimize real-world problems, including maximizing area and volume of geometric shapes and minimizing time or energy in river crossing and bird flight scenarios.

Learn to graph logarithms as the inverse of exponential functions, reflect them over the line y = x, and identify their asymptotes, domain, and intercepts.

Explore the circle equation in standard form, identify centers and radii, and convert from general to standard form by completing the square, with graphing techniques for center-radius visualization.

Learn the properties of ellipses, including center, foci, major and minor axes, and vertices, and how to derive and graph standard form equations.

Explore hyperbolas and compare them to ellipses. Learn standard forms, center, vertices, foci, and asymptotes, then practice graphing with guided examples.

Explore parabolas as conics with vertex, focus, directrix, axis of symmetry, horizontal or vertical opens via x squared equals 4 p y and y squared equals 4 p x.

Explore how angles are measured in degrees and radians, using standard position, positive and negative angles, and how to convert between degrees and radians while finding co-terminal and reference angles.

Learn the unit circle foundations for trigonometry, including cosine and sine as x and y coordinates, special right triangles, quadrant signs, radians, and applying arc length and sector area formulas.

Explore graphing sine and cosine from the unit circle, understanding amplitude, period, and phase shifts. Learn to apply horizontal and vertical transformations to sketch accurate trigonometric graphs.

Learn tangent and cotangent graphs as sine over cosine and cosine over sine, identify vertical asymptotes from zeros, note period pi, and apply basic transformations.

Examine how to make trig functions 1-to-1 by restricting domains to pass the horizontal line test, then evaluate sine, cosine, and tangent inverses with unit-circle examples.

Apply the law of cosines to solve triangles in side–side–side and side–angle–side cases, find sides and angles, and compute areas using Heron’s formula and 1/2 b c sin A method.

Explore the law of sines and the law of cosines through four real-world triangle problems, including computing angles, side lengths, and areas.