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# 2.6.1 graphing techniques translations

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### 2.6.1 graphing techniques translations

1. 1. Transformations – <br />*Vertical/Horizontal Translations<br />*Reflections about x-axis/y-axis<br />*Vertical or horizontal stretch/compression<br />2.6 Graphing Techniques<br />
2. 2. Translations – for any function y = f(x)<br />Vertical Translation – add any number k to the function. The graph of the function will translate k units in a vertical direction.<br />Each y value of the function will change by k units<br />Horizontal Translation – replace x with (x – h). The graph of the function will translate h units in a horizontal direction.<br />Each x value of the function will change by h units.<br />
3. 3. Reflections – for any function y = f(x)<br />About x-axis – Multiply the expression by -1. The graph of the function will be a reflection over the x-axis.<br />The y values will all be multiplied by -1<br />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.<br />The x values will be multiplied by -1<br />x-axis y-axis<br />
4. 4. Stretch/Compression – for any function y = f(x)<br />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) <br />The y values of the function will be multiplied by a.<br />
5. 5. Stretch/Compression – for any function y = f(x)<br />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)<br />The x values of the function will be multiplied by (1/b).<br />
6. 6. Summary…<br />Effects x-values<br />Effects y-values<br />
7. 7. Example…<br />Effects x-values<br />Effects y-values<br />
8. 8. Example…<br />Effects x-values<br />Effects y-values<br />
9. 9. Horizontal Translation +3<br />
10. 10. Vertical Translation -4<br />
11. 11. Reflection About x-axis<br />
12. 12. Reflection About y-axis<br />
13. 13. Write the equation resulting after the following transformations occur.<br />Translate 2 units down<br />Reflect about the x-axis<br />Translate 3 units left<br />Reflect about the y-axis<br />
14. 14. Write the equation resulting after the following transformations occur.<br />Reflect about the x-axis<br />Translate 2 units down<br />Reflect about the y-axis<br />Translate 3 units left<br />
15. 15. Assignment<br />p. 127 # 7 – 18, 19 – 33 odd<br />Do NOT use a calculator!<br />