Function Table Analysis: Determining if Y = -3 Represents a Function

Q: Can a function have the same y-value for different x-values?

Yes, absolutely! A function can have the same output (y-value) for multiple inputs (x-values). The key rule is that each input can only have one output.

Q: How is this different from a regular function?

It's still a regular function - just a special type called constant! The graph would be a horizontal line at $ y = -3 $.

Q: Would this still be a function if one y-value was different?

Yes! As long as each x-value has exactly one y-value, it's a function. It just wouldn't be a constant function anymore.

Q: Can I write this as an equation?

Absolutely! This constant function can be written as $ y = -3 $ or $ f(x) = -3 $.

Constant Functions with Table Analysis

Determine whether the following table represents a constant function:

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Step-by-step video solution

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00:00 Does the table represent a function?

00:03 A function has a constant slope, a constant difference between Y values

00:07 Let's look at the differences between Y values and try to find the slope

00:13 Therefore the slope equals the difference, a graph with a slope is a function

00:17 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Determine whether the following table represents a constant function:

Step-by-step solution

It is important to remember that a constant function describes a situation where, as the X value increases, the Y value remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, while the Y value remains constant.

Therefore, the table does indeed describe a constant function.

Final Answer

Yes, it does

Key Points to Remember

Essential concepts to master this topic

Definition: Constant function has same y-value for all x-values
Technique: Check if all y-values equal -3 in table
Check: Every x maps to y = -3, confirming constant function ✓

Common Mistakes

Avoid these frequent errors

Confusing function definition with constant function
Don't think a function needs different y-values = rejecting valid functions! This misunderstands that functions can have repeated outputs. Always remember that each x-value needs only ONE corresponding y-value, and constant functions are perfectly valid.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

FAQ

Everything you need to know about this question

Can a function have the same y-value for different x-values?

Yes, absolutely! A function can have the same output (y-value) for multiple inputs (x-values). The key rule is that each input can only have one output.

What makes this table represent a constant function specifically?

All the y-values are -3! In a constant function, no matter what x-value you choose, the output is always the same. Here, $f(x) = -3$ for all x-values.

How is this different from a regular function?

It's still a regular function - just a special type called constant! The graph would be a horizontal line at $y = -3$ .

Would this still be a function if one y-value was different?

Yes! As long as each x-value has exactly one y-value, it's a function. It just wouldn't be a constant function anymore.

Can I write this as an equation?

Absolutely! This constant function can be written as $y = -3$ or $f(x) = -3$ .

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