Increasing Function Analysis: Determining Possibility Between Two Points

Q: What exactly does 'increasing function' mean?

An increasing function means as you move from left to right on the graph (x gets larger), the y-values also get larger. Think of it like climbing uphill!

Q: How can I tell if two points allow an increasing function?

Compare the coordinates! If the right point has a larger y-value than the left point, you can draw an increasing line between them.

Q: Can a function be increasing if it has some flat parts?

Yes! A function can be non-decreasing (never going down) and still be considered increasing. The key is that it never decreases as x increases.

Q: What if the points have the same y-value?

If both points have the same y-value, the connecting line would be horizontal (neither increasing nor decreasing). This would be a constant function.

Increasing Functions with Point Analysis

Is it possible to create an increasing function with the two given points?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Can we create an increasing function from 2 points?

00:03 Let's complete the points for the graph

00:11 We can see that the function is increasing

00:16 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

Is it possible to create an increasing function with the two given points?

Step-by-step solution

We will begin by connecting the two points to each other, and subsequently we should see that we have obtained an increasing function.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Increasing function has y-values that rise as x-values increase
Method: Check if connecting points creates upward slope from left to right
Verify: If right point is higher than left point, function can increase ✓

Common Mistakes

Avoid these frequent errors

Confusing direction of increase
Don't assume a function is increasing just because it goes upward = wrong interpretation! You must check that as x increases (moves right), y also increases (moves up). Always compare coordinates: if x₂ > x₁ and y₂ > y₁, then increasing is possible.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

What exactly does 'increasing function' mean?

An increasing function means as you move from left to right on the graph (x gets larger), the y-values also get larger. Think of it like climbing uphill!

How can I tell if two points allow an increasing function?

Compare the coordinates! If the right point has a larger y-value than the left point, you can draw an increasing line between them.

Can a function be increasing if it has some flat parts?

Yes! A function can be non-decreasing (never going down) and still be considered increasing. The key is that it never decreases as x increases.

What if the points have the same y-value?

If both points have the same y-value, the connecting line would be horizontal (neither increasing nor decreasing). This would be a constant function.

Do I need to connect the points with a straight line?

Not necessarily! You can create an increasing function with curves too, as long as the overall trend goes upward from left to right.

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