Graphing Exponential Functions Using Tables and Equations

Miacademy & MiaPrep Learning Channel

This video provides a clear, step-by-step guide on how to graph exponential functions given an equation in the form y = ab^x. The lesson begins by analyzing the components of an equation to make predictions about the graph's shape, specifically identifying the y-intercept and the growth factor. It then demonstrates how to create a table of values to find specific coordinates, bridging the abstract equation with concrete data points. The video covers two distinct examples: one representing exponential growth and another representing exponential decay. It explicitly connects the algebraic "a" and "b" values to their visual representations on the graph and their numerical patterns in the table (common ratio). The narrator also addresses practical graphing skills, such as handling negative exponents and dealing with data points that may fall outside the visible scale of a standard graph grid. For educators, this video serves as an excellent core instruction piece for Algebra units on exponential functions. It reinforces prior knowledge of linear functions by contrasting "common difference" with "common ratio," helping students build on existing mental models. The clear visualization of how the table, equation, and graph relate makes it particularly useful for visual learners and for clarifying the behavior of asymptotic curves.