MAFS Algebra 1. Functions. Day 7 - Student Packet

Transcription

1 MAFS Algebra 1 Functions Day 7 - Student Packet

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3 Day 7: Functions MAFS.912.F-IF.1.2, MAFS.912.F-IF.1.1, MAFS.912.F-IF.2.5 I CAN evaluate functions that model a real-world context for inputs in the domain interpret the domain of a function within the real-world context given use function notation within the real-world context given use the definition of a function to determine if a relationship is a function, given tables, graphs, mapping diagrams, or sets of ordered pairs determine the feasible domain of a function that models a real-world context Representing, Naming, Evaluating Functions A relation is a set of ordered pairs. Function: A function is a correspondence between two sets, X Y, in which each element of X is matched to one only one element of Y. The set X is called the domain of the function. The domain is all the possible x-values (input values) of a function. If the domain is all real numbers, the function is continuous. If the domain is a particular set of numbers (such as whole numbers only), the function is discrete. The notation f: X Y is used to name the function describes both X Y. If x is an element in the domain X of a function f: X Y, then x is matched to an element of Y called f(x). We say f(x) is the value in Y that denotes the output of f corresponding to the input x. Range or Image of a Function: The range of a function f: X Y is the subset of Y, often denoted f(x), defined by the following property: y is an element of f(x) if only if there is an x in X such that f(x) = y. The range is all the possible y-values (output values) of a function. The range of the function depends on the domain. Algebraic Function: Given an algebraic expression in one variable, an algebraic function is a function f: D Y such that for each real number x in the domain D, f(x) is the value found by substituting the number x into all instances of the variable symbol in the algebraic expression evaluating. Vertical Line Test: When graphing a relation, the vertical line test can be used to see if the relation is a function. If you can draw a vertical line that crosses the graph in more than one place, the relation is not a function. 1

4 Problem Set 1. Which of the following are examples of a function? Justify your answers. a. The assignment of the members of a football team to jersey numbers. b. The assignment of U.S. citizens to Social Security Numbers. c. The assignment of students to locker numbers. d. The assignment of the residents of a house to the street addresses. e. The assignment of zip codes to residences. f. The assignment of residences to zip codes. g. The assignment of teachers to the students enrolled in each of their classes. h. The assignment of all real numbers to the next integer equal to or greater than the number. i. The assignment of each rational number to the product of its numerator denominator. 2. For each graph given match it to the contextual description that fits best. Then label the independent dependent axis with the proper variables. I. II. III. IV. V. A. The amount of money in a savings account where regular deposits some withdrawals are made. B. The temperature of the oven on a day that mom bakes several batches of cookies. C. The amount of gasoline on h at the gas station before a tanker truck delivers more. 3. Are the following relations functions? State the domain range. D. The number of watermelons available for sale at the farmer s market on Thursday. E. The amount of mileage recorded on the odometer of a delivery truck over a time period. a. *( ) ( ) ( ) ( )+ b. *( ) ( ) ( ) ( )+ c. *( ) ( ) ( ) ( )+ d. *( ) ( ) ( ) ( )+ e. *( ) ( ) ( ) ( )+ f. *( ) ( ) ( ) ( )+ 2

5 4. Determine whether the graphed relation is a function. State domain range. a. b. c. d. e. f. 3

6 5. Determine if the following relations are functions. State the domain range. a. b. c. d. e. f. x y x y Sequences are functions. The domain is the set of all term numbers (which is usually the positive integers), the range is the set of terms of the sequence. For example, the sequence 1, 4, 9, 16, 25, 36, of perfect squares is the function: Let : * + * } Assign each term number to the square of that number. a. What is ( )? What does it mean? b. What is the solution to the equation ( ) =? What is the meaning of this solution? c. According to this definition, is in the domain of? Explain why or why not. d. According to this definition, is in the range of? Explain why or why not. 4

7 7. Let ( ) =, let ( ) = ( ). Find the value of each function for the given input. a. ( ) b. ( ) c. ( ) d. ( ) e. ( ) f. ( ) g. ( ) h. ( ) i. ( ) ( ) j. ( ) ( ) k. ( ) ( ) l. ( ) ( ) 8. Since a variable is a placeholder, we can substitute letters that st for numbers in for. Let ( ) =, let ( ) = ( ), suppose, are real numbers. Find the value of each function for the given input. a. ( ) b. ( ) c. ( ) d. ( ) e. ( ) f. ( ) ( ) g. ( ) ( ) 9. What is the range of each function given below? a. Let ( ) =. b. Let ( ) = c. Let ( ) = d. Let ( ) = e. Let ( ) = such that is a positive integer. f. Let ( ) = for 10. Provide a suitable domain range to complete the definition of each function. a. Let ( ) =. b. Let ( ) = c. Let ( ) =, where ( ) is the number of calories in a swich containing grams of fat. 5

8 11. Given the function whose domain is the set of real numbers, let ( ) = if is a rational number, let ( ) = if is an irrational number. a. Explain why is a function. b. What is the range of? c. Evaluate for each domain value shown below. ( ) 2/3 0-5 π d. List three possible solutions to the equation ( ) =. For each situation either create a function or use the given function to find interpret solutions. 12. Fran collected data on the number of feet she could walk each second wrote the following rule to model her walking rate ( ) = a. What is Fran looking for if she writes ( ) =? b. In this situation what does ( ) = tell you? c. How can the function rule be used to indicate a time of 16 seconds was walked? d. How can the function rule be used to indicate that a distance of 200 feet was walked? 13. Ms. Callahan works hard to budget predict her costs for each month. She is currently attempting to determine how much her cell phone company will likely charge her for the month. She is paying a flat fee of $80 a month for a plan that allows for unlimited calling but costs her an additional twenty cents per text message. a. Write a function, ( ), for Ms. Callahan s current cell plan that will calculate the cost for the month based on the number of text messages she makes. b. Find ( ). c. Find ( ). d. Find ( ) = e. Find ( ) = f. At what number of texts would $20 unlimited texting be less expensive than her current plan? 14. Hope has been tracking the progress of her family as they travel across the country during their vacation she has created a function, ( ) = to model the progress they are making. a. What would Hope be attempting to find if she writes ( ) = ( )? b. What would ( ) = mean in this situation? c. What would ( ) mean in this situation? d. How could Hope use the function to find the time it would take to travel 800 miles? 6

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