Absolute value functions and transformations.notebook October 14, 2014 Absolute Value Functions and Graphs Objective: I can graph an absolute value function by performing transformations on the parent function f (x) = |x|. Oct 123:13 PM 1 Absolute value functions and transformations.notebook October 14, 2014 Vocabulary · The function f(x) = |x| is an absolute value function. · The highest or lowest point on the graph of an absolute value function is called the vertex. · An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. An absolute value graph has one axis of symmetry that passes through the vertex. Oct 123:15 PM 2 Absolute value functions and transformations.notebook October 14, 2014 Absolute Value Function · Absolute Value Function · Vertex · Axis of Symmetry Oct 123:18 PM 3 Absolute value functions and transformations.notebook October 14, 2014 Building the Absolute Value Function The absolute value function is defined by f (x) = |x|. Oct 123:21 PM 4 Absolute value functions and transformations.notebook October 14, 2014 This is the absolute value parent function. Table x f(x)=lxl y Oct 123:30 PM 5 Absolute value functions and transformations.notebook October 14, 2014 Parent Function · Vshape · It is symmetric about the yaxis (Axis of Symmetry) · The vertex is the minimum point on the graph Oct 123:34 PM 6 Absolute value functions and transformations.notebook October 14, 2014 Translation A translation is a transformation that shifts a graph horizontally or vertically, but doesn’t change the overall shape or orientation. Oct 123:35 PM 7 Absolute value functions and transformations.notebook October 14, 2014 Oct 1410:28 AM 8 Absolute value functions and transformations.notebook October 14, 2014 Oct 1410:31 AM 9 Absolute value functions and transformations.notebook October 14, 2014 Oct 1410:41 AM 10 Absolute value functions and transformations.notebook October 14, 2014 Oct 1410:30 AM 11 Absolute value functions and transformations.notebook October 14, 2014 Stretching and Compression The graph of y = a|x| is graph of y = |x| vertically stretched or compressed depending on the |a|. The value of a acts like the slope. Oct 123:37 PM 12 Absolute value functions and transformations.notebook October 14, 2014 Oct 1411:08 AM 13 Absolute value functions and transformations.notebook October 14, 2014 Oct 1411:10 AM 14 Absolute value functions and transformations.notebook October 14, 2014 Reflection The graph of y = a|x| is graph of y = |x| reflected across the xaxis. Oct 123:39 PM 15 Absolute value functions and transformations.notebook October 14, 2014 y = a |x – h| + k Oct 123:41 PM 16 Absolute value functions and transformations.notebook October 14, 2014 Multiple Transformations In general, the graph of an absolute value function of the form y = a|x – h| + k can involve translations, reflections, stretches or compressions. To graph an absolute value function, start by identifying the vertex Oct 123:50 PM 17 Absolute value functions and transformations.notebook October 14, 2014 Graphing Absolute Value Functions Graphing y = a|x – h| + k is straight forward: 1. Plot the vertex (h, k). (note…if +h inside that means h is negative(to the left); if – h inside that means h is positive (to the right) 2. Use the a value as slope to plot more points. Remember you have to do positive and negative slope to get points on both sides of the V 3. Connect the dots in a Vshape. Oct 123:50 PM 18 Absolute value functions and transformations.notebook October 14, 2014 Example 1 Graph the following function without making a table. y = |x – 2| + 3 Vertex How does this graph move? Did this graph stretch or compress? (slope of 1) Oct 123:52 PM 19 Absolute value functions and transformations.notebook October 14, 2014 Oct 123:56 PM 20 Absolute value functions and transformations.notebook October 14, 2014 Example 2 Graph the following function. y = (1/2)|x| Vertex How does this graph move? Did this graph stretch or compress? Oct 124:01 PM 21 Absolute value functions and transformations.notebook October 14, 2014 Your turn: y = (3/2)|x| Vertex ( , ) Translations Slope Oct 124:07 PM 22 Absolute value functions and transformations.notebook October 14, 2014 Your turn: y = 2|x + 2| 3 Vertex ( , ) Translations Slope Oct 124:11 PM 23 Absolute value functions and transformations.notebook October 14, 2014 write an abs value function that... Oct 1411:30 AM 24
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