5. Classify each of the following as a function, a partial function, or not a fu
ID: 3736203 • Letter: 5
Question
5. Classify each of the following as a function, a partial function, or not a function (If it's both a function and a partial function, choose "function"-the more exact classification.) and range a) t(1, a)j for domain space 1 space (a, b) b) f(x)-1/x when both domain and range space are the Real numbers (R) c) f(x) = sin(x) when domain space is the Natural numbers (N, the non-negative integers) and range space is R. d) f(x) = x2 when both domain and range space are R. (Recall that the square root of a positive number n is t n.) e) f(x, y) - max(x, y) for domain space R x R and range space R. f) f = {(-1, 1>, a), (, b), (, b)) for domain space 1, 2] x f1, 2] and range space (a, b) for domain space 1} x 11,2] and range space (a, b)Explanation / Answer
a) f = {(1, a)} for domain space {1} and range space {a, b}.
Answer: This is a function. Because here domain which is 1 is defined only once. And also function is defined for all domain.
b) f(x) = 1/x when both domain and range space are the Real numbers (R).
Answer: This is a partial function. Because firstly, f(x) does not have multiple values for a value of x. Secondly, f(x) is not defined for all value of x. Since 0 is real number but does not have any reciprocal.
c) f(x) = sin(x) when domain space is the Natural numbers (N, the non-negative integers) and range space is R.
Answer: It is a partial function. Because for a value of x, function f(x) does not have multiple values and it is not defined for all value of x.
d) f(x) = x½ when both domain and range space are R. (Recall that the square root of a positive number n is ±n.)
Answer: It is not a function. Because f(x) has more than one value for a single value of x. For example f(16) = +4 and -4 both.
e) f(x, y) = max(x, y) for domain space R × R and range space R.
Answer: It is a function because f(x) is defined for all values of x and f(x) does not have more than value for same value of x.
f) f = {(<1, 1>, a), (<2, 1>, b), (<1, 2>, b)} for domain space {1, 2} × {1, 2} and range space {a, b}.
Answer: It is a partial function because here not all domain are used like <2,2> is not there and none used more than once.
g) f = {(<1, 1>, a), (<1, 1>, b), (<1, 2>, b)} for domain space {1} ×× {1, 2} and range space {a, b}.
Answer: It is not a function because domain <1,1> is used more than once.
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