Does This Table Represent a Constant Function? Evaluating X(-1,0,1) with Y(2,4,7)

Q: What exactly makes a function constant?

A function is constant when every input gives the same output. For example, if x = -1, 0, and 1 all gave y = 3, then it would be constant.

Q: Do the x-values matter for determining if it's constant?

No! The x-values can be anything. Only the y-values matter. As long as all y-values are identical, the function is constant regardless of what the x-values are.

Q: What would the graph of this table look like?

Since the y-values are $2, 4, 7$, the graph would show three different points at different heights - definitely not a horizontal line like constant functions have.

Q: Is there a quick way to spot non-constant functions?

Absolutely! Just scan the y-values quickly. If you see any two different numbers, it's not constant. In this case: 2 ≠ 4, so we know immediately!

Constant Functions with Table Analysis

Determine whether the following table represents a constant function

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's see if this table shows a function.

00:15 Remember, a function has a constant slope, which means equal differences in Y values.

00:21 Now, let's check the changes in Y values to find the slope.

00:26 The differences vary, so the slope isn't constant. That means it's not a function.

00:32 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine whether the following table represents a constant function

Step-by-step solution

To determine if the table represents a constant function, we need to examine the Y-values corresponding to the X-values given in the table.

Step 1: Identify the given values from the table. The pairs are as follows: - For $X = -1$ , $Y = 2$ - For $X = 0$ , $Y = 4$ - For $X = 1$ , $Y = 7$
Step 2: Check if all Y-values are the same. Compare Y-values for each X-value:

Y = 2

X = -1

Y = 4

X = 0

Y = 7

X = 1

Since the Y-values (2, 4, and 7) are not the same, the function is not constant.

Thus, the table does not represent a constant function. The correct choice is: No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Constant function means all y-values must be identical
Technique: Compare y-values: 2, 4, 7 are clearly different
Check: If any two y-values differ, function is not constant ✓

Common Mistakes

Avoid these frequent errors

Confusing constant with continuous functions
Don't assume a table represents a constant function just because it shows smooth progression = wrong classification! Constant means y-values stay the same, not that values change smoothly. Always check if ALL y-values are identical.

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

What exactly makes a function constant?

A function is constant when every input gives the same output. For example, if x = -1, 0, and 1 all gave y = 3, then it would be constant.

Do the x-values matter for determining if it's constant?

No! The x-values can be anything. Only the y-values matter. As long as all y-values are identical, the function is constant regardless of what the x-values are.

Can a function be constant with just two points?

Yes! If you have two points like (-2, 5) and (3, 5), that portion shows constant behavior. But you'd need more information to know if the entire function is constant.

What would the graph of this table look like?

Since the y-values are $2, 4, 7$ , the graph would show three different points at different heights - definitely not a horizontal line like constant functions have.

Is there a quick way to spot non-constant functions?

Absolutely! Just scan the y-values quickly. If you see any two different numbers, it's not constant. In this case: 2 ≠ 4, so we know immediately!

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