Domain and Range Practice interactive worksheet - Free Printable

I will solve each problem on this "Domain and Range Practice" worksheet by carefully examining the sets of ordered pairs and the graphs provided. I'll explain the solution for each one.

Let's begin with the first problem in the top-left corner.

First Problem: Find the domain of {(-10, 6), (-9, 4), (-6, 9)}

- First, look closely: The domain of a set of ordered pairs is the set of all the x-coordinates (the first number in each pair). For this set, the x-coordinates are -10, -9, and -6.
- Next, find information: No external research is needed. This is a direct application of the definition of domain.
- Then, review the findings: The domain is simply the collection of these x-values.

The domain is {-10, -9, -6}.

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Second Problem: Find the domain of {(3, 4), (7, 5), (3, 6), (7, 7)}

- First, look closely: Again, the domain consists of the x-coordinates. Here, they are 3, 7, 3, and 7. Since a set contains unique elements, we list each value only once.
- Next, find information: No external research is needed.
- Then, review the findings: Even though 3 and 7 appear twice, the domain is still just the unique values.

The domain is {3, 7}.

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Third Problem: Find the range of {(3, 6), (5, 6), (9, 6)}

- First, look closely: The range is the set of all y-coordinates (the second number in each pair). Here, all the y-coordinates are 6.
- Next, find information: No external research is needed.
- Then, review the findings: All points have the same y-value, so the range is a single number.

The range is {6}.

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Fourth Problem: Find the range of {(5, -1), (5, 0), (5, 3)}

- First, look closely: The y-coordinates are -1, 0, and 3.
- Next, find information: No external research is needed.
- Then, review the findings: We collect all the unique y-values.

The range is {-1, 0, 3}.

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Fifth Problem: The domain of the function (top-right graph)

- First, look closely: I need to identify all the x-coordinates of the plotted points. Looking at the graph, the points are at x = 1, x = 2, x = 4, x = 5, and x = 6.
- Next, find information: No external research is needed; I can read the coordinates directly from the grid.
- Then, review the findings: The domain is the set of these x-values.

The domain is {1, 2, 4, 5, 6}.

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Sixth Problem: The domain of the function (middle-right graph)

- First, look closely: I need to identify the x-coordinates of the points on this graph. The points are at x = -4, x = -2, x = 2, and x = 3.
- Next, find information: No external research is needed.
- Then, review the findings: I will list these x-values to form the domain.

The domain is {-4, -2, 2, 3}.

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Seventh Problem: The range of the function (bottom-left graph)

- First, look closely: I need to identify the y-coordinates of the points. The points are at y = -4, y = 0, y = 1, y = 3, and y = -4 again (which is already listed).
- Next, find information: No external research is needed.
- Then, review the findings: The unique y-values are -4, 0, 1, and 3.

The range is {-4, 0, 1, 3}.

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Eighth Problem: The range of the function (bottom-right graph)

- First, look closely: I need to identify the y-coordinates of the points. The points are at y = -1, y = 0, y = 1, y = 2, y = 3, and y = 6.
- Next, find information: No external research is needed.
- Then, review the findings: I will list these unique y-values.

The range is {-1, 0, 1, 2, 3, 6}.

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Final Answer

Here are the solutions for all eight problems on the worksheet:

1. Domain of {(-10, 6), (-9, 4), (-6, 9)}: {-10, -9, -6}
2. Domain of {(3, 4), (7, 5), (3, 6), (7, 7)}: {3, 7}
3. Range of {(3, 6), (5, 6), (9, 6)}: {6}
4. Range of {(5, -1), (5, 0), (5, 3)}: {-1, 0, 3}
5. Domain of the function (top-right graph): {1, 2, 4, 5, 6}
6. Domain of the function (middle-right graph): {-4, -2, 2, 3}
7. Range of the function (bottom-left graph): {-4, 0, 1, 3}
8. Range of the function (bottom-right graph): {-1, 0, 1, 2, 3, 6}