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Exploring Piecewise & Absolute Value Functions

Learn about piecewise functions defined by multiple equations and absolute value functions with V-shaped graphs. Understand domains, ranges, and how to graph them effectively.

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Exploring Piecewise & Absolute Value Functions

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  1. Lesson 2-3: Piecewise and Absolute Value Functions Advanced Math Topics

  2. Piecewise functions • A function defined by two or more equations • Each equation applies to a different part of the domain • Domain • it is usually described in the problem and can just be rewritten for the answer • Range • found by taking the endpoints (if there are any) for the domain intervals and plugging them into the appropriate function to find the y-values

  3. f(x)= different things for different sections of the graph Remember what open dots and closed dots mean?? Summary

  4. Piece Wise Functions Step 1Graph the linear function f(x)= –1 for x ≤3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

  5. Step 2Graph the constant function f(x)= –1 for x > 3. Since x does not satisfy this inequality, begin with an open circle at (3, –1) and draw a horizontal ray to the right.

  6. Answer:The function is defined for all values of x, so the domain is all real numbers. The values that are y-coordinates of points on the graph are all real numbers less than or equal to 2, so the range is {y | y ≤ 2}.

  7. A. B. C. D.

  8. Absolute Value Function • A function with a variable inside the absolute value bars • The graph makes a “V” shape

  9. To Graph • Take everything inside the | | and set it equal to 0. The x-value you get is the x-value for the corner. • Plug the x-value in and solve for y • The resulting ordered pair is where you absolute value graph starts! (the corner) • Plug in two x-values on either side of the corner to find ordered pairs to finish the graph

  10. To Find Domain and Range • Domain: ARN there are no restrictions on the x-values you can plug into an absolute value graph • Range: determined from the y-values, y will be > or < the y-value of the corner

  11. Summary

  12. Absolute Value

  13. Graphs

  14. Graph f(x) = |x| – 2 and g(x) = |x| + 3 on the same coordinate plane. Which answer choice is not true about the pair of graphs?

  15. Identify the type of function

  16. Identify the type of function

  17. Identify the type of function

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