Exploring Transformations of Parent functions af(b(x-c)) +d

Master function transformations! Learn how a, b, c, and d shift, stretch, and reflect parent functions.

Review Quadratic Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Absolute Value Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Cubic Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Square Root Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Cube Root Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Rational Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d Exponential Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d. Logarithmic Transformations Use the Desmos graph to explore how a, b, c, and d affect the function af(x), f(b), f(x-c) and f(x)+d What happened when you change the "a" or "b" value? If a<0, a negative number, the graph reflects across the x-axis. When a >1 , the graph stretches vertically. On the other hand, when 0<a<1, the graph compresses vertically. If b<0, a negative number, the graph reflects across the y-axis. When b >1 , the graph compresses horizontally. On the other hand, when 0<b<1, the graph stretches horizontally. What happened when you change the "c" or "d" value? When c>0, as in f(x-c), the graph translates right. When c<0, as in f(x+c), the graph translates left. When d>0, as in f(x)+d, the graph translatesup. When d<0, as in f(x)-d, the graph translates down. Parent Functions Transformations Summary This video is totally optional. It is not your notes. REFLECTION: How did using the desmos sliders and watching this video help you to understand transformations of functions? What helped you the most? What questions do you still have? What did you learn about transformations? (write a paragraph - 5 sentences)