Inverse Variation and the Reciprocal Function

In this video, I start with a quick review of direct variation, reminding students that in this type of relationship, as one variable increases, the other increases at a constant rate. This sets the stage for the main focus: understanding inverse variation and how it behaves differently. I explain that in inverse variation, as one variable increases, the other decreases, and the product of the two values remains constant. I show how to recognize an inverse variation in tables, graphs, or verbal descriptions by identifying this opposite relationship. From there, I introduce the reciprocal parent function, which has two curved branches that appear in opposite quadrants of the graph and never touch the horizontal or vertical axes—these axes act as invisible boundaries, or asymptotes. Once the basic shape is understood, I move into how the graph changes with h and k shifts. These shifts move the entire graph left or right and up or down, which also changes the location of the asymptotes. I guide students through how to identify these shifts and graph them accurately by tracking where the new asymptotes are placed and how the curve follows them.