Comparing Graphs of Logarithmic Functions | Reflections & Transformations pre-calculus 12 Algebra II
This video from the MathSupport channel ( @mathsupportnow ) explores the comparison between the graph of y = log₂(x) and y = log₀.₅(x), focusing on their algebraic relationships, graphical transformations, and reflections. You’ll learn how the base of a logarithm affects the graph’s shape, direction, and position, and how to interpret these changes both visually and algebraically. We’ll also break down how fractional bases create reflections, how vertical stretches and shifts work, and how these transformations impact the domain, range, and asymptotes. What You Will Learn: ✅Comparison between y=log₂(x) and y=log₀.₅(x) ✅How changing the base affects the graph’s reflection ✅Algebraic relationship between log₀.₅(x) and log₂(x) ✅Using change of base rule for fractional bases ✅Reflections over the x-axis and y-axis for log graphs ✅How inverse relationships with exponentials affect logs ✅Applying vertical stretches and vertical shifts to logs ✅Shifting asymptotes and interpreting transformations ✅Domain and range changes after transformations Who This Video Is For: 🎯Students learning logarithmic functions and transformations 🎯High school and college math learners in Algebra or Precalculus 🎯BC Math Curriculum students 🎯Teachers explaining graphing of logs 🎯Anyone curious about how base changes alter logarithmic graphs 00:00–Introduction and Objectives 00:22–Comparing Graphs y=log₂(x) and y=log₀.₅(x) 01:38–Algebraic Relationship Using Change of Base Rule 03:12–Reflections and Inverse Relationships with Exponentials 03:38–Reflection Over Axes Explained 04:50–Graphical Representation in Desmos 06:03–Transformation Analysis (Stretch, Shift, Reflection) 07:54–Domain and Range Changes 👍Like if you found the graph comparison helpful 🔔Subscribe for more graphing and algebra tutorials 💬Comment with questions about logarithmic transformations 📤Share with classmates or math learners More Video lesson about Function Transformation: • Graphing Exponential functions with Horizo... • Final Exam Review Questions - Function Tra... #LogarithmicFunctions #mathsupport #mathhelp #canadianmath #precalculus
