TOPICS COVERED ON “Functions” TEST: Study Guide/ practice “Functions Test” Name: Date: Note: The pages in this packet are meant for additional practice. Students are NOT expected to complete every problem in the packet. Rather, students should use these pages as a resource-- in addition to studying the notes and past quizzes. It is suggested that students complete several problems from each of the following pages in order to be fully prepared for test. TOPICS COVERED ON “Functions” TEST: Vocabulary: Function-- a special type of relation where every member of the Domain is paired with exactly __________member of the Range. In other words, there can never be a repeating __________ value in the same relation. Domain Range Independent Variable Dependent Variable Sequences (Arithmetic and Geometric) Identifying a Function Solving Linear Functions Graphing Linear Functions Four Ways to Represent a Function (Equation, Words, Table, Graph) Real-Life Function Scenarios NOTES SPACE/HELPFUL TIPS (to be filled out in class):

sequences Sequence Fill-in-the-Blanks: An arithmetic sequence is a sequence where the next term is found by either adding or __________________________________ by the SAME #, and the “rule” for determining what comes next is described as the common _______________________________ . A geometric sequence is a sequence where the next term is found by either multiplying or __________________________________ by the SAME #, and the “rule” for determining what comes next is described as the common _______________________________ . Sequence Rule (Common Diff. or Ratio) What Comes next? Arithmetic or Geometric? Variable Expression 1) -5, -3, -1, 1, 3 . . . 2) 1, 3, 9, 27 . . . 3) 16, 8, 4, 2, 1, ½ . . . 4) 2, -6, 18, -54. . . 10, 6, 2, -2, -6 . . . Multiple Choice: 1) Which of the following sequences is a geometric sequence? 1, -4, 16, -64 . . . 2, 4, 6, 8. . . 2, -2, -6, -10 . . . 2) What would be the 6th term of the following arithmetic sequence? 4, 1, -2, -5 . . . -8 -11 8 Which variable term describes what would come next in the following sequence? 6, 2, -2, -6 . . . x + 4 4x x – 4 What is the common difference in the following arithmetic sequence? 1, -4, -9, -14 . . . -5 5 C. 1/5 What is the common ratio in the following geometric sequence? 50, 10, 2, 2 /5 . . . 1/5

Identifying a function Fill-in-the-Blanks: A function is a special type of ______________________________________ where every member of the Domain is paired with exactly __________member of the Range. In other words, there can never be a repeating ______________________ value in the same relation. 1. Which of the following relations is not a function? 2. Which of the following relations is a function? 3. Which of the following is NOT a function? 4. Which of the following is a function? 5. Which of the following is NOT a function?

CAREFUL . . . Can you use the shortcut for #3 and #4??? Linear Equations (from a table . . .) Write the linear equation that represents each of the following function tables: 1) y = ________________ 2) 3) 4) 5) 6) 7) 8) x y 1 5 2 10 3 15 x y -1 3 4 1 5 2 6 x y -2 -5 -1 1 4 x y -1 1 2 3 5 x y 4 1 8 2 12 3 16 x y -1 -3 1 3 2 6 x y -2 -5 -1 3 1 7 x y 6 1 4 2 3 Remember the shortcut: Find the pattern going down “y” & use the “magic #” to MULTIPLY to the “x” #!! Which linear equation matches the following function tables? 1) y = x + 1 y = x + 2 y = 2x + 2 2) y = x – 3 y = -3x + 5 y = x + 5 3) y = x – 6 y = x + 8 y = 4x 4) y = x + 9 y = 2x + 4 y = 3x + 1 x -1 1 2 3 y 4 6 8 x -2 -1 1 2 y 11 8 5 x -2 2 4 6 y -8 8 16 24 x 3 6 9 12 15 y 10 19 28 37 46 CAREFUL . . . Can you use the shortcut for #3 and #4???

SOLVING Linear Equations Solve the following linear equations: Equation Table y = x – 3 y = -3x + 4 3) x = 4y + 6 Equation Table 4) y = - x + 5 5) y = 4x - 6 6) x = 2y – 4 x y -1 1 2 x y -1 1 2 x y -4 -2 2 x y -4 -2 2 x y -24 -12 12 x y -8 -4 4

Graphing linear equations Solve and graph the following linear equations: 1) 2) x y = 5x - 4 y -1 1 2 x y = - x + 3 y -1 1 2 3) y = 2x - 3 4) x = y - 4 x y -2 2 4 x y -2 2 4

Function representations Fill-in-the-Blanks: There are _____________________________ ways to represent a function. We can use an equation, words, a table, or a graph. If we are given one representation, we can use that information to find the other three ways to represent the function. Equation Words Table Graph 1) y = 3x -2 2) “y is equal to twice a number, minus four.” 3) 4) x y x y x y -3 1 2 3 6 x y

Multiple choice (miscellaneous)

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12) 13) 14)

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