Section 1.2: What is a Function? y = 4x y is the dependent variable because it depends on what x is. x is the independent variable because any value can be chosen to replace x. Domain: a set of values which are reasonable substitutions for the independent variable, input values (x-values) Range: output values (the "y" values) Function: A relation where each element in the domain is paired with one and only one element in the range. (the "x" values do not repeat) Aug 31 10:31 AM 1
Section 1.2: What is a Function? Dependent Variable The variable which represents the values that are effected by the other quantity. The variable that represents the output values of the relationship. The second variable in an ordered pair. Independent Variable The variable which represents the values that cause the other quantity to change. The variable that represents the input values of the relationship. The first variable in an ordered pair. Function: A relation where each element in the domain( ) corresponds to one and only one element in the range( ). (the independent variable does not repeat) Aug 31 10:14 PM 2
Statement of a function relation: The dependent variable is a function of the independent variable. OR Is the dependent variable a function of the independent variable? When the relationship between two variables is a function, we say that the dependent variable is a function of the independent variable. Ways to describe functions: with formulas or tables Aug 31 10:55 PM 3
Domain of a function: The set of values that are allowed to be substituted for the independent variable. (input values that are allowed) Range of a function: The set of values of the dependent variable that can result from the allowable substitutions for the independent variable. (output values) Aug 31 11:06 PM 4
Yes, each member of the domain(months) corresponds to one and only one member of the range(temperature) No, at least one member of the domain (Temperature) corresponds to more than one member of the range(months) Jan 18 7:44 AM 5
What is the generic ordered pair? For part i Domain: is all the months of the year Range: is 73, 74, 76, 77, 78, 79, 80, 81 Jan 18 7:45 AM 6
Includes zero with the natural numbers The whole numbers and their opposites ratio of integers a and b so b The set of Irrational numbers ex: π, 2.74920438293... non repeating or non terminating decimals numbers that can be represented by decimals. All the rational and irrational numbers combined. Aug 31 11:18 PM 7
What is the generic ordered pair? Yes, each member of the domain(# of Cans) corresponds to one and only one member of the range(cost) Domain:{v v is a whole number} Range: {c c is a non negative multiples of 59} Jan 18 7:46 AM 8
The domain and range of a relation is the key idea. They are used to determine if a relation is a function or not. A function is a relation in which each member of the domain corresponds to exactly one member of the range. The different number sets are possible domain and range sets as well. Variables stand for numbers and are often replaced with values from the domain resulting in the values of the range. Jan 18 7:46 AM 9
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Examples: Domain, Range, and Function Examples: Domain, Range, and Function State the Domain, Range, and if it's a function. 1. { (0, 1), (2,6), (3,7)} 2. {(1, 4), (2, 4), (3, 4)} 3. {(7, -6), (-4, 7), (7, -8), (2, 3)} 4. Mapping: D -6-4 R 0 1 2 Aug 31 10:47 AM 20
Real Number System Real Number System Rational #'s: repeating or terminating decimals ex: 2/3, 1/2, 4, 10.2 Irrational #'s: non-repeating or nonterminating decimals ex: π, 2.74920438293... Integers: {...-3, -2, -1, 0, 1, 2, 3,...} Whole #'s: {0, 1, 2, 3,...} Natural #'s: {1, 2, 3,...} Aug 31 11:23 AM 21
Examples Continued... Examples Continued... 5. The table below shows the average temperature T in degrees Fahrenheit for each month M in Honolulu, Hawaii. M Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec T 73 73 74 76 78 79 80 81 81 80 77 74 a.) Is T a function of M? Justify your answer. b.) Is M a function of T? Justify your answer. 6. Give the domain and range of the function above. (part a) Aug 31 11:34 AM 22
7. The total cost c of v cans of vegetable soup at $.59 per can is given by the formula c = 59v. a.) Is c a function of v? Why or why not? b.) What are the domain and range of this function? Aug 31 11:34 AM 23
1 1 to 1 9 Lesson Masters (B).pdf 1 1 to 1 9 Lesson Masters (B) SOLUTIONS.pdf Sep 7 7:07 AM 24
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Yes, each member for the domain (a) corresponds to one and only one member fo the range(b) (a, b) Sep 8 10:42 AM 28
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Attachments 1 1 to 1 9 Lesson Masters B.pdf 1 1 to 1 9 Lesson Masters B SOLUTIONS.pdf