Determine whether the following table represents a function
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Determine whether the following table represents a function
It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.
In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3
Therefore, according to the rule, the table describes a function.
Yes
Determine whether the following table represents a constant function:
No! Functions don't require patterns. The y-values can be any numbers as long as each x-value maps to exactly one y-value. Random outputs like (1→5), (2→100), (3→2) still make a valid function.
That's perfectly fine for functions! Multiple inputs can have the same output. For example: (1→5), (2→5), (3→7) is still a function because each x-value has only one corresponding y-value.
Look at the x-column only! If you see any repeated x-values, it's not a function. In our table: -1, 0, 1 are all different, so it is a function.
The explanation talks about patterns, but that's extra information. The real test is unique x-values. Even if there were no pattern (like -1→5, 0→2, 1→99), it would still be a function!
If any x-value appeared twice with different y-values, like:
Then x=1 would map to both 11 and 20, violating the function rule.
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