Grade 11 General Math Q1 Lesson 1 - Define & Evaluate Function PDF

GRADE 11! GENERAL Q1 -WEEK 1 WARM-UP EXERCISE GET YOUR PAPER & BALLPEN Set your stopwatch to 0. Solve the following manually (no calculator) in a 1 whole piece of paper. Write the time spent (in mins) in solving on the lower right portion of your paper. 1.2𝑥 2 (3y)(4xy) 2.7xyz (2𝑥 2...

GRADE 11! GENERAL Q1 -WEEK 1 WARM-UP EXERCISE GET YOUR PAPER & BALLPEN Set your stopwatch to 0. Solve the following manually (no calculator) in a 1 whole piece of paper. Write the time spent (in mins) in solving on the lower right portion of your paper. 1.2𝑥 2 (3y)(4xy) 2.7xyz (2𝑥 2 y)(3𝑦 9 𝑧 6 ) 24𝑥 2 𝑦 3 (2𝑥 8 ) 3. 6𝑥𝑦2 9𝑎7 𝑏 (3𝑎6 𝑏2 ) 4. 18𝑎5𝑏3 7(𝑥 4 )3 5. (3𝑥 2)2 7 3 6. (5z ) 7.995 x 866 8.851 / 48 (round to nearest hundredths place) a.represent real-life situations using functions, including piece-wise functions; b.evaluate a function;  Q1-LESSON 1.1: Representing Real- Life Situations Using Functions, including piecewise functions  What have you remembered about relations and functions? A relation is any set of ordered pairs or a relationship between set of values. The set of all first elements of the ordered pairs is called the domain of the relation, and the set of all second elements is called the range. A function is a relation in which each element in the domain corresponds to exactly one element in the range. Domain/first element should appear once only.  To further understand function, let’s study the following: Given the following ordered pairs, which relations are functions? A = {(1,2), (2,3), (3,4), (4,5)} B = {(3,3), (4,4), (5,5), (6,6)} C = {(1,0), (0, 1, (-1,0), (0,-1)} D = {(a,b), (b, c), (c,d), (a,d)} Domain/first element should appear once only.  A = {(1,2), (2,4), (3,4), (4,5)} B = {(3,3), (4,4), (5,5), (6,6)} The relations A and B are functions because each element in the domain corresponds to a unique element in the range. C = {(1,0), (0, 1, (-1,0), (0,-1)} D = {(a,b), (b, c), (c,d), (a,d)} Meanwhile, relations C and D are not functions because they contain ordered pairs with the same domain: C = (0,1) and (0,-1) D = (a,b) and (a,d) How about from the given table of values, which relation shows a function? A and B are functions since all the values of x corresponds to exactly one value of y. Unlike table C, where -1 corresponds to two values, 4 and 1. We can also identify a function given a diagram. On the following mapping diagrams, which do you think represent functions? The relations A and C are functions because each element in the domain corresponds to a unique element in the range However, B is a mere relation and not function because there is a domain which corresponds to more than one range.  How about if the given are graphs of relations, can you identify which are functions? Do you still remember the vertical line test? A relation between two sets of numbers can be illustrated by graph in the Cartesian plane, and that a function passes the vertical line test. A graph of a relation is a function if any vertical line drawn passing through the graph intersects it at exactly one point. Using the vertical line test, can you identify the graph/s of function?  A and C are graphs of functions B and D are not because they do not pass the vertical line test. In Mathematics, we can represent functions in different ways. It can be represented through words, tables, mappings, equations and graphs.  You have learned that function can be represented by equation. Since output (y) is dependent on input (x), we can say that y is a function of x. For example, if a function machine always adds three (3) to whatever you put in it. Therefore, we can derive an equation of x + 3 = y or f(x) = x+ 3 where f(x) = y. There are functions that requires more than one formula in order to obtain the given output. There are instances when we need to describe situations in which a rule or relationship changes as the input value crosses certain boundaries. In this case, we need to apply the piecewise function. A piecewise function is a function in which more than one formula is used to define the output. Each formula has its own domain, and the domain of the function is the union of all these smaller domains. We notate this idea like this:  Example 1: A videoke machine can be rented for P1,000 for three days, but for the fourth day onwards, an additional cost of P400 per day is added. Represent the cost of renting a videoke machine as a piecewise function of the number of days it is rented. For three- day rent  Example 2: A certain chocolate bar costs ₱50.00 per piece. However, if you buy more than 5 pieces they will mark down the price to ₱48.00 per piece. Use a piecewise function to represent the cost in terms of the number of chocolate bars bought. 50n if  Example 3: The cost of hiring a catering service to serve food for a party is ₱250.00 per head for 50 persons or less, ₱200.00 per head for 51 to 100 persons, and ₱150.00 per head for more than 100. Represent the total cost as a piecewise function of the number of attendees to the party. 250n, 0 < n ≤ 50 200n, 150n, ORAL RECITATION PART 1 Direction: Identify the following statement if it is true or false. 1. A relation is a set of ordered pairs where the second element is called the domain while the first element is called the range 2. A function can be classified as one-to-one correspondence, one-to-many correspondence and many- to-one correspondence. 3. In a function machine, the input represents the independent variable while the output is the dependent variable. ORAL RECITATION PART 2 Direction: Read each situation carefully to solve each problem. 1.A person is earning ₱750.00 per day to do a certain job. Express the total salary S as a function of the number n of days that the person works 2. A computer shop charges ₱15.00 in every hour of computer rental. Represent your computer rental fee (R) using the function R(t) where t is the number of hours you spent on the computer. 3. A tricycle ride costs ₱10.00 for the first 2 kilometers, and each additional kilometer adds ₱8.00 to the fare. Use a piecewise function to represent the tricycle fare (F) in terms of the distance d in kilometers.  Q1-LESSON 1.2: Evaluating Functions We can evaluate a function by replacing the variable with the values of the domain Evaluate Kevin’s savings for 10 days. input process output ORAL RECITATION PART 3 ACTIVITY #1 Direction: Evaluate the following in a one whole piec. 1. 2. 3. 4. 5. 6. 7. 8. greatest integer function, value was rounded-off to the real number to the integer less than the number ACTIVITY #1