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Please help! For each of the following relations, identify whether it’s a function or not and why, then state the domain and range.

Please help! For each of the following relations, identify whether it’s a function-example-1
User Aneury
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Answer:

The first one is a function, the second one is a function, and the third one is not a function.

Domain for the first one, just list the x values. Same for range.

Domain and range for the second one are both all real numbers.

For the last one, solve the quadratic, and find the vertex. The range will be all numbers greater than the y on the vertex, while the domain is all real numbers.

Explanation:

An easy way to tell if something is a function or not is to check that each input (or x-value) has a different output (or y-value.) The first one is not a function because in the table, we see that 1 gives an output of 9, but later on you see 1 also gives an output of 20.

If you're ever given a graph and asked this question, do the vertical pencil test. Start at the left of the graph, and slide your pencil over the graph (vertically) and if your pencil ever hits more than one point at a time, it's not a function. Hope this helped!

User Jzapata
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