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.

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.

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.

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