What is a function? In your book, you will find: A function f is a rule that assigns to each element x in a set D exactly one element, called f ( x ), in a set E .
What is a function? It is somewhat better to say less:
What is a function? It is somewhat better to say less: A function f is a rule that assigns to each element x in a set D exactly one element, called f ( x ), in a set E .
What is a function The difference between these arises when considering the question of whether two functions are the same.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers:
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7,
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7, so we get 7.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7, so we get 7. Rule 2.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7, so we get 7. Rule 2. Add the digits together. Repeat until the result has fewer than one digit.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7, so we get 7. Rule 2. Add the digits together. Repeat until the result has fewer than one digit. E.g., 421 → 4 + 2 + 1 = 7.
What is a function The difference between these arises when considering the question of whether two functions are the same. For instance, consider the following two ‘rules’, which can be applied to positive integers: Rule 1. Divide by 9 and consider the remainder. E.g., 421 = 46 × 9 + 7, so we get 7. Rule 2. Add the digits together. Repeat until the result has fewer than one digit. E.g., 421 → 4 + 2 + 1 = 7. In fact, though these look like rather different rules, in fact they always produce the same result. In mathematics, we say they give the same function.
What is a function?
What is a function? A function f assigns to each element x in a set D exactly one element, called f ( x ), in a set E .
What is a function? A function f assigns to each element x in a set D exactly one element, called f ( x ), in a set E . The set D is called the domain, and the set E is called the codomain. One says f is a function from D to E .
What is a function? A function f assigns to each element x in a set D exactly one element, called f ( x ), in a set E . The set D is called the domain, and the set E is called the codomain. One says f is a function from D to E . In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are.
Domain
Domain In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are.
Domain In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are. In practice this is rarely done explicitly.
Domain In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are. In practice this is rarely done explicitly. Indeed in all the examples previously, we did not specify either the domain or the codomain.
Domain In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are. In practice this is rarely done explicitly. Indeed in all the examples previously, we did not specify either the domain or the codomain. In fact, you will often encounter questions like: What is the domain of the function √ x
Domain What is the domain of the function √ x Strictly speaking, this question is somewhat ambiguous.
Domain What is the domain of the function √ x Strictly speaking, this question is somewhat ambiguous. Indeed, to give √ x as a function,
Domain What is the domain of the function √ x Strictly speaking, this question is somewhat ambiguous. Indeed, to give √ x as a function, I should have told you what its domain was.
Domain What is the domain of the function √ x Strictly speaking, this question is somewhat ambiguous. Indeed, to give √ x as a function, I should have told you what its domain was. You should interpret this question as asking “what is the largest subset of the real numbers on which the formula √ x makes sense and defines a function”.
Domain What is the domain of the function √ x Strictly speaking, this question is somewhat ambiguous. Indeed, to give √ x as a function, I should have told you what its domain was. You should interpret this question as asking “what is the largest subset of the real numbers on which the formula √ x makes sense and defines a function”. The answer is: [0 , ∞ ).
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x .
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x . The domain of this function would be [1 , ∞ ),
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x . The domain of this function would be [1 , ∞ ), because that’s what I said the domain was.
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x . The domain of this function would be [1 , ∞ ), because that’s what I said the domain was. The domain is part of the data included in the function.
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x . The domain of this function would be [1 , ∞ ), because that’s what I said the domain was. The domain is part of the data included in the function. However, when a function is given by a formula and the domain is not explicitly specified,
Domain To belabor the point, I can define a function f ( x ) from say [1 , ∞ ) to the real numbers, given by the formula f ( x ) = √ x . The domain of this function would be [1 , ∞ ), because that’s what I said the domain was. The domain is part of the data included in the function. However, when a function is given by a formula and the domain is not explicitly specified, we understand the domain to be the largest possible such that the formula makes sense.
What is a function? A function f assigns to each element x in a set D exactly one element, called f ( x ), in a set E . The set D is called the domain, and the set E is called the codomain. One says f is a function from D to E . In particular, to precisely specify a function, one is strictly speaking supposed to say what the domain D and codomain E are.
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