How to Graph Exponential Functions Step-by-Step

Miacademy & MiaPrep Learning Channel

This instructional video provides a step-by-step guide on how to graph exponential functions. Hosted by a narrator named Justin, the lesson begins by outlining a consistent three-step process: plotting the y-intercept based on the initial value, multiplying by the growth factor to find points to the right, and dividing by the growth factor to find points to the left. The video emphasizes understanding the behavior of the function rather than just plugging in numbers blindly. The content progresses through three distinct examples of increasing difficulty. The first example demonstrates a simple integer base ($2^x$), the second introduces decimal growth factors ($1.25^x$) requiring a calculator, and the third tackles the complex topic of fractional exponents (e.g., $x/2$). This final section explains a powerful algebraic "trick" of converting fractional exponents into roots (like square roots) to make calculating integer steps easier. For educators, this video serves as an excellent direct instruction tool or review resource for Algebra units. It is particularly valuable for its visual demonstration of how exponential curves are generated point-by-point and for its clear explanation of the connection between fractional exponents and radicals. The inclusion of the "move left by dividing" concept helps reinforce the inverse relationship between multiplication and division within exponential growth contexts.