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Determine whether each relation represents a function.For each function, State the domain and the range.

(a) {(2,5),(4,6),(6,7),(8,8)}

(b) {(1,3),(4,-2),(-3,5),(1,7)}

(c)


(d)

Short Answer

Expert verified

Part a. The relation is a function and its domain is given by the set 2,4,6,8and the range is given by the set 5,6,7,8.

Part b. The relation is not a function.

Part c. The relation is not a function.

Part d. The relation is a function whose domain is the set of all real numbers and its range is given by the set [2,∞).

Step by step solution

01

Part (a) Step 1. Check the ordered pairs

For the first relation, {(2,5),(4,6),(6,7),(8,8)}there are no ordered pairs with the same first element and different second elements.

So the given relation is a function.

The domain is the set of first elements of ordered pairs and it is given as 2,4,6,8.

The range is given by the set of second elements of ordered pairs and it is given as 5,6,7,8.

02

Part (b) Step 1. Check the ordered pairs 

The relation(1,3),(4,-2),(-3,5),(1,7)is not a function because there are two ordered pairs, (1,3)and (1,7), that have the same first element and different second elements.

03

Part (c) Step 1. Perform vertical line test

For the given graph, we draw a vertical line as

So it can be seen that a vertical line intersects the graph at more than one point. So the graph is not the graph of a function.

04

Part (d) Step 1. Perform vertical line test

For the given graph, we draw a vertical line as

It can be seen that each vertical line intersects the graph at atmost one point.

So the given graph is the graph of a function.

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