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Algebra 1: Chapter 4, An Introduction to Functions Study Guide Study Guide for Chapter 4 Test: Friday, December 4th 4.1: Using Graphs to Relate Two Quantities - Be able to represent mathematical relationships using graphs. Directions: Sketch a graph to represent each situation. Label each situation. The number of pounds compared to the total cost Your pulse rate as you watch a scary movie 4.2: Patterns and Linear Functions - Be able to identify and represent patterns that describe linear functions. Directions: For each table below, determine whether the relationship is a linear function. Then represent the relationship using words, an equation, and a graph. X/Y Table: X 0 1 2 3 Y -3 2 7 12 Gas in Tank Table: Miles Traveled, X 0 17 34 51 Answer: Words: Answer: Words: Equation: Equation: Graph: Graph: Gallons of Gas, Y 11.2 10.2 9.2 8.2 4.3: Patterns and Nonlinear Functions - Be able to identify and represent patterns that describe nonlinear functions. Directions: Each set of ordered pairs represents a function. Write a rule that represents the function. What is the rule for the function represented by the ordered pairs (1, 2), (2, 16), (3, 54), (4, 128), (5, 250)? What is the rule for the function What is the rule for the function represented by the ordered pairs (- represented by the ordered pairs 2, 1), (-1, -2), (0, -3), (1, -2), (2, 1)? (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25)? 4.4: Graphing a Function Rule - Be able to graph equations that represent functions. Directions: Graph each function rule. y = 10x y = 9 – 2x y = 3x + 2 4 4.5: Writing a Function Rule - Be able to write equations that represent functions. Directions: Write a function rule that represents each situation. C is 8 more than half of n. 2.5 more than the quotient of h and 3 is w. The price (p) of a pizza is $6.95 plus $.95 for each topping (t) on the pizza. The almond extract (a) remaining in an 8-ounce bottle decreases by 1/6 ounce for each batch (b) of waffle cookies made. 4.6: Formalizing Relations and Functions - Be able to determine whether a relation is a function and be able to find the domain and range and use a function notation. Directions: Find the domain and range of each relation. Identify the domain and range: {(6, -7), (5, -8), (1,4), (7, 5)} Identify the domain and range: {(4, 2), (1,1), (0,0), (1, -1), (4, -2)} Is this relation a function? Is this relation a function? Find the range of each function for the given domain: g(x) = -4x + 1 {-5, -1, 0, 2, 10} Find the range of each function for the given domain: f(x) = 8x -3 { -1/2, ¼, ¾, 1/8} 4.7: Arithmetic Sequences - Be able to identify and extend patterns in sequences and to represent arithmetic sequences using function notation. Directions: Tell whether the sequence is arithmetic. If it is, identify the common difference. -9, -17, -26, -33, … 2, 11, 21, 32, … 0.2, 1.5, 2.8, 4.1, … 15, 14.5, 14, 13.5, 13, … ***If you have any questions, please see Ms. Magan for help prior to the test!!! ***