1. Transformations – *Vertical/Horizontal Translations *Reflections about x-axis/y-axis *Vertical or horizontal stretch/compression 2.6 Graphing Techniques
2. Translations – for any function y = f(x) Vertical Translation – add any number k to the function. The graph of the function will translate k units in a vertical direction. Each y value of the function will change by k units Horizontal Translation – replace x with (x – h). The graph of the function will translate h units in a horizontal direction. Each x value of the function will change by h units.
3. Reflections – for any function y = f(x) About x-axis – Multiply the expression by -1. The graph of the function will be a reflection over the x-axis. The y values will all be multiplied by -1 About the y-axis – replace the x in the function with (–x). The graph of the function will be a reflection over the y-axis. The x values will be multiplied by -1 x-axis y-axis
4. Stretch/Compression – for any function y = f(x) Vertical – multiply any number a (except zero), called a scalar. The graph of the function will be stretched vertically or compressed vertically depending on the absolute value of the scalar (absolute values greater than 1 will stretch, less than 1 will compress) The y values of the function will be multiplied by a.
5. Stretch/Compression – for any function y = f(x) Horizontal – replace x with (bx). The graph of the function will be compressed or stretched horizontally depending on the absolute value of b (absolute values greater than 1 will compress, less than 1 will stretch) The x values of the function will be multiplied by (1/b).
13. Write the equation resulting after the following transformations occur. Translate 2 units down Reflect about the x-axis Translate 3 units left Reflect about the y-axis
14. Write the equation resulting after the following transformations occur. Reflect about the x-axis Translate 2 units down Reflect about the y-axis Translate 3 units left
