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1 Rev -5-6 Name Date TI-84 GC Graphing Piecewise Functions Objectives: Use TEST to compare a single value o a variable to a test value Use TEST to compare many values o a variable to a test value Multiply a unction by a TEST result to limit domain and graph a piece Determine i your GC will show y 0 when multiplied, use divide by a TEST result Add pieces to graph a piecewise unction The TEST menu is the second unction above MATH: We can select rom the list by typing the corresponding number. Less than is option 5, or eample. Eample : Use GC to determine i a 6< 0 b 6 a Use the TEST menu to determine i 6< 0 The GC says i the answer to the question is true or yes. 6< 0 is a true statement, so GC says. b Use the TEST menu to determine i 6 The GC says 0 i the answer to the question is alse or no. 6 is a alse statement, so GC says 0. Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

2 Rev -5-6 TI-84 GC Graphing Piecewise Functions page Eample : Use GC to store in memory and determine i a < 0 b Store in memory location graphing. a Test < 0 The GC tests the value stored in memory, and concludes that yes, < 0. b Test The GC tests the value stored in memory, and concludes that no, is a alse statement. Eample : Graph the TEST results or a 4 b > CAUTION: We are NOT graphing the inequality 4, which would be graphed on a number line. TEST gives y-coordinate that is 0 or, depending on whether is less than or equal to 4 y-coordinate or not less than or equal to 4 y-coordinate 0. The GC automatically generates the values o rom Xmin and Xma in WINDOW. a Type the test 4as a unction in the menu, then graph in a standard viewing window. Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

3 Rev -5-6 TI-84 GC Graphing Piecewise Functions page Eample, continued The GC graphs a horizontal line y or all values up to 4, then a horizontal line y 0 or all -values ater 4. It s hard to tell what it did at eactly 4 without checking a table. 4 has y-value. b Type the test > as a unction in the menu, then graph in a standard viewing window. The GC graphs a horizontal liney 0 or all values beore, then a horizontal line y or all - values ater -. The table shows that is assigned y-coordinate 0. Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

4 Rev -5-6 TI-84 GC Graphing Piecewise Functions page 4 Eample 4: Graph the unction or the domain 0by multiplying by the TEST results or its domain. CAUTION: We want the unction value times the test value, so we need to include additional parentheses! CAUTION: I you have a new color calculator, you may see a horizontal liney 0 or the -values on the right side o the graph. You can remove this by DIVIDING by the test value. Newer calculators do not graph values that result in 0. Keystrokes and screenshot or dividing by the test value: CAUTION: However, i you have an older calculator, dividing by the test value will completely conuse your calculator and it may graph nothing at all! Eample 5: Graph the piecewise unction results or its domain using two lines o the y menu. 0 by multiplying each piece by TEST > 0 The irst piece is the same as Eample 4. We continue with the second piece in y : Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

5 Rev -5-6 TI-84 GC Graphing Piecewise Functions page 5 Eample 5, continued CAUTION: When you transer this graph to paper, you must clearly indicate which piece includes its endpoint closed circle and which piece does not open circle! REMEMBER: A piecewise unction is still a single unction, and the resulting graph must pass the vertical line test! Eample 6: Graph the piecewise unction <. 4 We epect the irst piece to be a horizontal line while the second piece is a parabola. Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

6 Rev -5-6 Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students. TI-84 GC Graphing Piecewise Functions page 6 Practice: Graph the piecewise unction. Graph < Graph > 4 Graph > 5 4 Graph < Graph > 6 Graph < 7 Graph < 9 7

7 Rev -5-6 TI-84 GC Graphing Piecewise Functions Solutions, page Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.

8 Rev -5-6 Copyright 06 by Martha Fidler Carey. Permission to reproduce is given only to current Southwestern College instructors and students.