How to Find Positive and Negative Intervals on Function Graphs

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide on how to identify and write positive and negative intervals for function graphs using interval notation. Building on previous knowledge of increasing and decreasing intervals, the narrator explains the core definitions: positive intervals occur where the function's output is above the x-axis, and negative intervals occur where the output is below it. The video emphasizes the critical rule that points where the output is exactly zero are excluded from both categories. The video walks through three progressive examples: a simple linear function, a downward-opening parabola, and a more complex polynomial function that touches the x-axis without crossing it. Through these examples, students learn how to read the graph from left to right, identify x-intercepts as boundaries, and correctly apply interval notation using parentheses to exclude zeros. The final example specifically addresses the common "tricky" scenario where a function touches the x-axis and bounces back, requiring the interval to be split to exclude that single point. For educators, this video serves as an excellent direct instruction tool for Algebra units covering function characteristics. It visually reinforces the connection between the graph's position relative to the x-axis and algebraic interval notation. The inclusion of a "pause and try" moment allows for immediate formative assessment, making it suitable for flipped classrooms, review sessions, or as a primary method for introducing the concept of analyzing function behavior.