Questions: Determine whether the relation is a function. Identify the domain and the range. [ (4,16),(6,24),(7,28) ] Is the relation a function? No Yes

Determine whether the relation is a function. Identify the domain and the range.
[
(4,16),(6,24),(7,28)
]

Is the relation a function?
No
Yes

Transcript text: Determine whether the relation is a function. Identify the domain and the range. \[ \{(4,16),(6,24),(7,28)\} \] Is the relation a function? No Yes

Solution

Solution Steps

Step 1: Check if the relation is a function

To determine if the relation is a function, verify that each input \( x \) in the relation corresponds to exactly one output \( y \). In the given relation: \[ \{(4,16),(6,24),(7,28)\} \]

\( 4 \) maps to \( 16 \),
\( 6 \) maps to \( 24 \),
\( 7 \) maps to \( 28 \).

Since no \( x \)-value is repeated, the relation is a function.

Step 2: Identify the domain

The domain of a relation is the set of all \( x \)-values. From the relation: \[ \{(4,16),(6,24),(7,28)\} \] The domain is: \[ \{4, 6, 7\} \]

Step 3: Identify the range

The range of a relation is the set of all \( y \)-values. From the relation: \[ \{(4,16),(6,24),(7,28)\} \] The range is: \[ \{16, 24, 28\} \]

Final Answer

The relation is a function: Yes.
Domain: \( \{4, 6, 7\} \)
Range: \( \{16, 24, 28\} \)

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