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What I Have Learned A. Based on the concepts that you learn from this module, complete the following: 1-2. A relation is a function if it is a and 3. (2,3) (3,4) and (4,5) represents a type of function. Given the table below. Months of plants grown (x) 2 3 4 PROPE SALE Height of the plants in cm (f(x)) 21 31 41 FOR ERNMENT Is the given a one to one function? Make a function that represents the given situation. 6 . Interchanging the x and y-values of a one-to-one function would result to a 7. The inverse of f is denoted by _ 8. A function has an inverse if and only if it is 9. for all x in the domain of f-1 10 for all x in the domain of f. B. Below is the graph of the function f(x) = x + 3. Find its inverse, complete its set of values, and represent it with a graph. (Construct the graph in the same plane below.) f-1 (x ) = x 1 2 3 4 5 What I Can Do This section involves real-life application of the inverse of a one-to-one function. Read and understand the problem carefully and show your complete solution. A. Theresa's mother asked her to buy dressed chicken. If a kilo of dressed chicken costs Php 180, how many kilos she can buy if her mother gave her Php 450? Is the given situation represents a one to one function? If yes, generate a function that represents the situation. Solution: B. Below is the graph of a function and its inverse. Is the original function one-to- one? Explain your thoughts. GOVERNMENT PROF NOT FOR SALE f ( x ) = _ C. 1. Find the domain and range of the inverse function x , whose graph is shown below.GO NO Is the given a one to one function? uIA Make a function that represents the given situation. 6 . Interchanging the x and y-values of a one-to-one function would result to a 7. The inverse of f is denoted by 8. A function has an inverse if and only if it is for all x in the domain of f-1 10 for all x in the domain of f. B. Below is the graph of the function f(x) = x + 3. Find its inverse, complete its set of values, and represent it with a graph. (Construct the graph in the same plane below.) f-1 (x ) = X 1 2 3 4 5 old What I Can Do This section involves real-life application of the inverse of a one-to-one function. Read and understand the problem carefully and show your complete solution. A. Theresa's mother asked her to buy dressed chicken. If a kilo of dressed chicken costs Php 180, how many kilos she can buy if her mother gave her Php 450? Is the given situation represents a one to one function? If yes, generate a function that represents the situation. Solution: B. Below is the graph of a function and its inverse. Is the original function one-to- one? Explain your thoughts. GOVERNMENT PROPERTY NOT FOR SALE f ( x ) = _ C. 1. Find the domain and range of the inverse function x , whose graph is shown below. 2. Find the domain and range of the inverse function f(x)=-x+1 3x+ 2 f ( x ) = 3 3. Find the domain and range of the function inverse x-4A. f(x) = x C. f(x) = x-1 B. f(x) = 1 D. f(x) = x+1 4. Complete the statement: A function is one to one if: A. exactly one domain corresponds to exactly one range B. there is two domains in one range. C. in every domain there corresponds two ranges. D. many domain and many range. 5. Complete the statement: (-1,2) (1,2) (2,2) is: A. one to one C. many to one B. one to many D. many to many 6. A function with an inverse is described to be A. one-to-many C. many-to-one B. one-to-one D. many-to-many 7. The inverse of an inverse f-1(x) is A. x B. 1 C. f-1(x) D. f(x) GOVERNMENT PROPERTY NOT FOR SALE 8. What is the result if a function that is not one-to-one is inverted? A. not a function B. a function C. a relation D. not a relation 9. f-1(f (x)) =_ for all x in the domain of f. A. y B. x C. 1 D. O 10. Complete the statement: The inverse of a one-to-one function can be interpreted as the same function , that is, it is a function from a y-value back to its corresponding x-value. A. but in the same direction B. but in the same value C. but in the opposite direction D. but in the same value TRUE OR FALSE. Write TRUE if the statement is correct and FALSE if the statement is wrong. 1 1. A function has an inverse if it is one-to-many. 12. Given the graph of one-to-one function, the graph of its inverse can be obtained by reflecting the graph about the line. 13. This example is one-to-one? The relation pairing an SSS member to his or her SSS number. 14. The domain of a function is the set of all values that the variable can take. 15. The range of the function is the set of all values that will take. Additional Activities This section includes supplementary activities related to the inverse of a one-to-one function. 1. Graph y = f-1(x) if the graph of y = f(x) = 2x +5 restricted in the domain (x|-2 5 x $ 1.5]]. a. What is the range of the function? b. What is the domain and range of its inverse? 2. Dan can paint the room in 3 hours, Jill can paint the same room in 5 hours. How long will it take to paint the room if they work together? GOVERNMENT PROPERTY NOT FOR SALEAdditional Activities This section includes supplementary activities related to the inverse of a one-to-one function. 1. Graph y = f-1(x) if the graph of y = f(x) = 2x +5 restricted in the domain (x|-2