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Common Core Algebra Unit 16: Other Types of Functions 5/4/17Lesson 3: Absolute Value FunctionsObjective: SWBAT graph absolute value functions.Do Now: Complete the table of values for the parent function, f(x) = |x| ( |x| is found under the MATH Key: MATH ? NUM ? 1:abs). Use the table of values to complete the graph.xf(x)31286452603500-3-2-10123What is the minimum value of the function? ___________State the domain: _________________ State the range: __________________State the domain over which the function is increasing. ________________State the domain over which the function is decreasing. ________________Absolute Value FunctionsOne of the most recognized piecewise defined functions is the absolute value function.When finding the range of an absolute value function, find the vertex (the turning point).? If the graph opens upwards, the range will be greater than or equal to the y-coordinate of the vertex.? If the graph opens downward, the range will be less than or equal to the y-coordinate of the vertex.The average rate of change is constant on each straight-line section (ray) of the graph.Partner Practice:Graph the following:1. f(x) = 2|x|2. f(x) = 2|x|365760015811500228600158115003. f(x) = -|x|4. f(x) = ?|x|2286008890003657600-381000Turn and Talk:For graphs of absolute value functions in the form y = a|x| , how does a affect the graph?Lesson Summary:An?absolute value function?is a?function?that contains an algebraic expression within?absolute value?symbols.?Problem Set:1. Which is the graph of ?a) b) c) d) 2. Which graph represents the equation ?a) b) c) d) 3. What is the minimum value of the function ?1)2)23)34)4. On the set of axes below, graph the function .State the range of the function. State the domain over which the function is increasing.5. Dominick graphs the equation where a is a positive integer. If Gina multiplies a by , the new graph will become1)narrower and open downward2)narrower and open upward3)wider and open downward4)wider and open upward6. Graph and label the functions and on the set of axes below.Explain how increasing the coefficient of x affects the graph of .7. On the axes below, graph .If , how is the graph of translated to form the graph of ? If , how is the graph of translated to form the graph of ?8. Graph the function on the set of axes below.Explain how the graph of has changed from the related graph .9. On the set of axes below, graph . Include the interval . ................
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