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QuestionList the ordered pairs for the function ff and specify its domain and range: f(1)=10,f(2)=−6,f(3)=3f(1)=10, f(2)=-6, f(3)=3.

Studdy Solution

STEP 1

Assumptions1. The function ff is defined at three points 1,,31,,3. . The corresponding function values are 10,−6,310, -6,3 respectively.

STEP 2

We can write the function as a set of ordered pairs where the first element of each pair is an input to the function and the second element is the corresponding output.
f={(x,f(x))∣x∈{1,2,}}f = \{(x, f(x)) | x \in \{1,2,\}\}

STEP 3

Substitute the given function values into the set.
f={(1,f(1)),(2,f(2)),(3,f(3))}f = \{(1, f(1)), (2, f(2)), (3, f(3))\}

STEP 4

Substitute the given function values into the set.
f={(1,10),(2,−6),(3,3)}f = \{(1,10), (2, -6), (3,3)\}

STEP 5

The domain of a function is the set of all possible inputs, in this case, the first elements of each ordered pair.Domain={x∣(x,y)∈f}Domain = \{x | (x, y) \in f\}

STEP 6

Substitute the given ordered pairs into the domain.
Domain={1,2,3}Domain = \{1,2,3\}

STEP 7

The range of a function is the set of all possible outputs, in this case, the second elements of each ordered pair.Range={y∣(x,y)∈f}Range = \{y | (x, y) \in f\}

STEP 8

Substitute the given ordered pairs into the range.
Range={10,−6,3}Range = \{10, -6,3\}So, the function ff as a set of ordered pairs is {(1,10),(2,−6),(3,3)}\{(1,10), (2, -6), (3,3)\}, the domain of ff is {1,2,3}\{1,2,3\}, and the range of ff is {10,−6,3}\{10, -6,3\}.

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