Determine Which Table Corresponds with the Given Graph

Q: How can I tell if a graph shows a constant function?

Look for a perfectly horizontal line! If the line goes straight across without going up or down, it represents a constant function where the y-value never changes.

Q: What should all the y-values look like in the table?

All y-values must be exactly the same number. For example: if your line is at height 4, then every y-value should be 4, no matter what the x-values are.

Q: Why do the x-values change but y-values stay the same?

That's how constant functions work! The input (x) can be anything, but the output (y) is always the same value. It's like a machine that always gives the same result no matter what you put in.

Q: What's the difference between this and a vertical line?

A vertical line has the same x-value for all points (like x = 3), while a horizontal line has the same y-value for all points (like y = 4). Vertical lines aren't functions!

Constant Functions with Horizontal Line Graphs

Given the following graph, determine which table corresponds to the following table

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate table

00:04 Let's find points on the graph to determine the graph equation

00:20 This is the function equation

00:24 We'll deduce the appropriate table from the equation

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the following graph, determine which table corresponds to the following table

Step-by-step solution

To solve this problem, observe that the graph represents a horizontal line at some constant $y$ -value.

We need to identify which table reflects this characteristic, meaning the $y$ -values must all be the same for listed $x$ -values. Let's evaluate the choices:

Choice 1: $y$ -values are 2, 3, 4 for $x = -1, 0, 1$ . This is not constant.
Choice 2: $y$ -values are 4, 4, 4 for $x = -1, 0, 1$ . This represents a constant function where $y$ is always 4.
Choice 3: $y$ -values are 5, 8, 11 for $x = -1, 0, 1$ . This is not constant.
Choice 4: $y$ -values are 3, 8, 13 for $x = -1, 0, 1$ . This is not constant.

The choice that matches the graph, depicting a horizontal line at a consistent $y$ -value, is Choice 2. Therefore, the table corresponding to the graph is:

Final Answer

Key Points to Remember

Essential concepts to master this topic

Horizontal Lines: Represent constant functions where y-value never changes
Table Pattern: All y-values identical: (-1,4), (0,4), (1,4) shows y=4
Verification: Check every y-value in table matches horizontal line height ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal and vertical lines
Don't think a horizontal line means x-values stay the same = wrong table choice! Horizontal lines have constant y-values, not constant x-values. Always remember: horizontal lines cross the y-axis at one point and extend left-right with same height.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

How can I tell if a graph shows a constant function?

Look for a perfectly horizontal line! If the line goes straight across without going up or down, it represents a constant function where the y-value never changes.

What should all the y-values look like in the table?

All y-values must be exactly the same number. For example: if your line is at height 4, then every y-value should be 4, no matter what the x-values are.

Why do the x-values change but y-values stay the same?

That's how constant functions work! The input (x) can be anything, but the output (y) is always the same value. It's like a machine that always gives the same result no matter what you put in.

Can a horizontal line go through negative y-values?

Absolutely! A horizontal line can be at any height: positive, negative, or zero. The key is that all points on the line have the same y-coordinate.

What's the difference between this and a vertical line?

A vertical line has the same x-value for all points (like x = 3), while a horizontal line has the same y-value for all points (like y = 4). Vertical lines aren't functions!

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