Increasing Function Domain: Analyzing Graph from x=-2 to x=8

Q: How do I tell if a function is increasing from a table?

Look at consecutive points and check if both x and y values go up together. If x increases but y decreases (like from x=3 to x=5), the function is decreasing in that interval.

Q: What does the notation 1.5 > x > 0 mean?

This means x is between 0 and 1.5, not including the endpoints. It's the same as writing 0 . The function increases in this entire interval.

Q: Why isn't the whole graph increasing?

Functions can have different behaviors in different intervals. This function increases from x=0 to x=1.5, but then decreases after x=1.5. That's why we need to identify specific domains.

Q: Do I need to include the endpoint values?

Look carefully at the inequality symbols! while ≤ means 'less than or equal to' (include). Here, $ 1.5 > x > 0 $ doesn't include x=0 or x=1.5.

Q: What if the y-values are the same for different x-values?

If y-values stay the same as x increases, the function is constant (neither increasing nor decreasing) in that interval. Only count intervals where y-values actually rise.

Function Behavior with Coordinate Analysis

In which domain is the function increasing?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find where the function increases.

00:07 A function increases when both the X and Y values grow together.

00:13 Starting here, the function begins to go up.

00:18 Here, the function starts to go down again.

00:27 We can see this is where the function increases.

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In which domain is the function increasing?

Step-by-step solution

Remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

According to the given value table, we can see that in the domain where $1.5 > x > 0$ the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$1.5 > x > 0$

Final Answer

$1.5>x>0$

Key Points to Remember

Essential concepts to master this topic

Rule: Function increases when both x and y values increase together
Technique: Compare consecutive points: from (0,0) to (1,1) to (1.5,2)
Check: Verify y-values rise as x-values rise in your interval ✓

Common Mistakes

Avoid these frequent errors

Confusing where function increases vs decreases
Don't look at just x-values or y-values alone = wrong intervals! This ignores how the function actually behaves between points. Always check that BOTH x and y increase together in your chosen domain.

Practice Quiz

Test your knowledge with interactive questions

Does the function in the graph decrease throughout?

FAQ

Everything you need to know about this question

How do I tell if a function is increasing from a table?

Look at consecutive points and check if both x and y values go up together. If x increases but y decreases (like from x=3 to x=5), the function is decreasing in that interval.

What does the notation 1.5 > x > 0 mean?

This means x is between 0 and 1.5, not including the endpoints. It's the same as writing 0 < x < 1.5. The function increases in this entire interval.

Why isn't the whole graph increasing?

Functions can have different behaviors in different intervals. This function increases from x=0 to x=1.5, but then decreases after x=1.5. That's why we need to identify specific domains.

Do I need to include the endpoint values?

Look carefully at the inequality symbols! < means 'less than' (don't include) while ≤ means 'less than or equal to' (include). Here, $1.5 > x > 0$ doesn't include x=0 or x=1.5.

What if the y-values are the same for different x-values?

If y-values stay the same as x increases, the function is constant (neither increasing nor decreasing) in that interval. Only count intervals where y-values actually rise.

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