Question

find the domain of the function defined by the set of points below. express your answer as a set of numbers. (5,7),(-10,-8),(10,-4),(-1,5),(3,-2),(6,-8) answer

Explanation:

Step1: Recall the definition of the domain of a function defined by a set of points.

The domain of a function given as a set of ordered pairs \((x, y)\) is the set of all the \(x\)-values (the first elements) of the ordered pairs.

Step2: Identify the \(x\)-values from each ordered pair.

For the ordered pairs \((5,7)\), \((-10,-8)\), \((10,-4)\), \((-1,5)\), \((3,-2)\), \((6,-8)\):

• From \((5,7)\), the \(x\)-value is \(5\).
• From \((-10,-8)\), the \(x\)-value is \(-10\).
• From \((10,-4)\), the \(x\)-value is \(10\).
• From \((-1,5)\), the \(x\)-value is \(-1\).
• From \((3,-2)\), the \(x\)-value is \(3\).
• From \((6,-8)\), the \(x\)-value is \(6\).

Step3: Collect these \(x\)-values into a set.

We collect the \(x\)-values: \(-10\), \(-1\), \(3\), \(5\), \(6\), \(10\). Then we form a set with these values, making sure each value is unique (which they already are in this case).

Answer:

\(\{-10, -1, 3, 5, 6, 10\}\)