4 Problems TRIGONOMETRY Senior Year Hish School

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4 TRIGONOMETRY PROBLEMS • Show every step of the work. Do not omit any detail • The Graph needs to be done in the Word Assignment: Relations and Functions A relation is any set of ordered pairs. The set of all the first components of the ordered pairs is called the domain. The set of all the second components of the ordered pairs is called the range. A relation in which each member of the domain corresponds to exactly one member of the range is called a function. There are many ways to display relations and functions. They may be displayed as sets of ordered pairs, with a mapping diagram, as lists of domain and range elements, or with a coordinate graph. Equations may also be described using function notation. For example, f ( x ) = 2 x + 3 is an equation written using function notation. Functions given in this notation may be combined using addition, subtraction, multiplication, and division. Additionally, two or more functions may be described as being functions of one another using composition of functions. NEXT PAGE Assignment: Relations and Functions Follow the directions to solve all the parts of each problem. Show all work leading to your answer. 1. There are many ways to describe relations and function. Consider the relation shown as a set of ordered pairs: {( 2,3 ) , ( −1,5 ) , ( 4,3 ) , ( 0,5 ) , ( 3, −2)} a. Describe this relation in three different ways: • Make a mapping diagram. • List the domain and range in set notation. • Graph the points in the coordinate plane. y 6 4 2 -6 -4 -2 2 4 6 x -2 -4 -6 b. Does this relation represent a function? How do you know? 2. Create a relation of 5-8 ordered pairs similar to those given to you in problem 1.Your relation should be written using proper set notation as shown in the example problem. Describe this new relation in three different ways: • Make a mapping diagram. • List the domain and range in set notation. • Graph the points in the coordinate plane. y 6 4 2 -6 -4 -2 2 4 6 -2 -4 -6 b. Does this relation represent a function? How do you know? x 3. Functions can be combined using addition, subtraction, multiplication, and division. Consider the two functions described below. f ( x ) = 2x + 3 g( x ) = 4x − 5 a. Perform each of the following operations using the functions f(x) and g(x) listed above. Show all work. • f ( x ) + g( x ) • g( x ) + f ( x ) • f ( x ) − g( x ) • g( x ) − f ( x ) b. In previous math courses, you may have learned that the commutative property states that the order of two or more mathematical properties may be reversed. For example, multiplication of integers is commutative as illustrated by the fact that 2 • 5 = 10 and 5 • 2 = 10. Using your answers from 3a above, do you think that addition and/or subtraction of functions is commutative? Explain your answer. Provide an example for both addition and subtratrion. 4. Two or more functions may be shown as functions of one another. Again, consider the two functions shown below; f ( x ) = 2x + 3 g( x ) = 4x − 5 a. Using these functions, compute each of the following. Show all work. • f (g ( x )) • g (f ( x )) b. Based on your results from 4a, consider the following statement. “Another student in your math class says that when performing compositions of functions, the order in which two functions are combined does not matter. They insist that f ( g ( x ) ) is the same as g ( f ( x )) ” How would you respond to this student? Write a response with examples to explain why your classmate is correct or incorrect.
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1. The relation is {( 2,3 ) , ( −1,5 ) , ( 4,3 ) , ( 0,5 ) , ( 3, −2 )}
a. Mapping diagram:

The domain: {2, −1, 4, 0, 3}, the range: {3, 5, −2}.
Points on the plane:

b. This relation does represent a function, because any x has only one corresponding y.

2. The relation is...


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