Precalculus Course

This video on precalculus covers a wide range of topics starting with the introduction of functions, their domains, and ranges. functions are seen as rules mapping inputs to outputs, and function notation like f(x) represents the output value of y. Evaluating functions involves plugging in values for x. functions can be represented by equations or graphs, with the vertical line test used to determine if a graph represents a function. The domain is all possible x values, and the range is the y values that make sense for the function. functions can be classified based on their graphs and symmetry. Toolkit functions and transformations, including reflections and stretches, were discussed.

Topics Covered

• Introduction to functions, domains, and ranges
• function notation and evaluation
• Representation of functions by equations or graphs
• vertical line test for functions
• Classification of functions based on graphs and symmetry
• Toolkit functions and transformations
• trigonometry: solving trigonometric equations, sine, cosine, tangent
• law of cosines for non-right triangles
• hyperbolas: definition, major and minor axes, vertices, center, asymptotes
• Shifting the center, finding vertices and focuses, graphing hyperbolas
• polar coordinates, converting between polar and Cartesian coordinates
• Parametric equations and the difference quotient for functions