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Warm Up/Do Now Solve the following: Numbers 1-5 are all equal to positive numbers once the absolute value bars are alone. Why is this? What would happen if they were equal to negative numbers? Absolute Value Functions Chapter 2 Warm Up/ Do Now Solve & Graph Solution on a Number Line ① | 2x + 3 | < 6 ④ | x | + 4 < 12 ② | 2x – 3 | > 5 ⑤ -3 + | x – 2 | > 5 ③ | 10 + 4x | < 14 ⑥ | x + 1| < -6 Solve the following: | x + 2 |< -1 NO SOLTUION!!!! Absolute values always end up positive so there is no way the absolute value of |x+2| could be less than negative 1. Solve the following: | x + 2 |< -1 NO SOLTUION!!!! Absolute values always end up positive so there is no way the absolute value of |x+2| could be less than negative 1. Solve the following: | x - 2 |> -3 ALL REAL NUMBERS!!!! Absolute values are always greater than any negative number! Parent Function: • • • • • f(x) = |x| V-shape It is symmetric about the y-axis The vertex is (0,0) Doman: (-∞, ∞) Range: [0, ∞) The Absolute Value Function The graph of f(x) = a|x – h| + k is the graph of y = |x| translated h horizontal units and k vertical units and stretched by a. • The new vertex is at (h, k) IF the equation has +h you need to make it a negative in the vertex!!! When k is on the right, you keep its sign! Graphing Absolute Value Functions y = a|x – h| + k 1.Plot the vertex (h, k) 2.Use the a value as slope to plot points on the right side 3.Use symmetry to find corresponding point on the left side 4.Connect the dots in a V-shape Remember: If a is positive if the graph goes up If a is negative if the graph goes down Graph f(x) = 3|x + 4| 1. Plot the vertex 2. Use a as a slope to move left & right vertex = (-4, 0) a=3 Finding an Equation from a Graph Find the vertex coordinate (1, -4) so h is 1 and k is -4 Find a by counting the slope from the vertex to another point to the right slope = 2/1 so a is 2 So the equation is: y = 2|x – 1| - 4 Plug h, k, and a into y = a|x – h| + k Write the equation for: y = -|x +2| + 3 Real Life! Lets graph it in a calculator! Exit Slip • You will be handed an exit slip. • Complete it without using any notes or asking for help. • Once finished, bring it to me to be checked. • Good luck!