Math  /  Data & Statistics

QuestionWhich of the following relations represent functions? Select all that apply.
\begin{tabular}{|c|c|c|c|c|c|} \hlinexx & -2 & -1 & 0 & 1 & 2 \\ \hlineyy & 3 & 3 & 3 & 3 & 3 \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? Does each xx value have only *one* corresponding yy value? Watch out! A function can have the same yy value for different xx values, but not the other way around!

STEP 2

1. Check for unique x values.
2. Verify function definition.

STEP 3

Let's **carefully examine** the table.
Notice that each xx value is **unique**: -2, -1, 0, 1, and 2.
No xx value appears more than once!
This is a good start.

STEP 4

Now, let's **check** if each of these unique xx values maps to exactly *one* yy value.
Look at our table.
When xx is -2, yy is 3.
When xx is -1, yy is 3.
And so on!
Every xx value corresponds to *one and only one* yy value (which happens to be 3 in this case).

STEP 5

Remember, it's perfectly fine for different xx values to have the same yy value.
Think of the function f(x)=3f(x) = 3.
No matter what you plug in for xx, the output is always 3!
That's a perfectly valid function.

STEP 6

This relation *is* a function!
Each xx value has only one corresponding yy value.

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