Function Domain Analysis: Finding Intervals Where Function is Increasing

Q: What's the difference between increasing and decreasing?

Increasing: As x gets bigger, y gets bigger too. Decreasing: As x gets bigger, y gets smaller. Think of walking uphill vs. downhill!

Q: Can a function be increasing in some parts and decreasing in others?

Absolutely! Most functions have different behaviors in different intervals. That's why we specify the domain where it's increasing, like $ x > 0 $.

Q: Why does the answer say x > 0 instead of x < 0?

Look carefully at the table! For x > 0 (positive values): x = 0→2→4 and y = 4→5→6 (increasing). For x

Q: What if two y-values are the same?

If consecutive y-values are equal, the function is constant in that interval (neither increasing nor decreasing). Look for sections where y-values actually change.

Function Analysis with Increasing Intervals

In which domain is the function increasing?

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Step-by-step video solution

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00:00 Find the domain of increase of the function

00:03 The function increases when X and Y values increase simultaneously

00:12 From this point the function begins to increase

00:21 We can deduce from this the domain of increase

00:31 And this is the solution to the question

Step-by-step written solution

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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 $0 > x$ X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x > 0$

Final Answer

$x>0$

Key Points to Remember

Essential concepts to master this topic

Increasing Function: Both x and y values rise together simultaneously
Reading Tables: Compare consecutive points: x = 0→2→4, y = 4→5→6
Verification: Check all x > 0 pairs show y-values increasing ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing with decreasing intervals
Don't look at where y-values are largest = wrong intervals! This misses the actual rate of change pattern. Always compare how y-values change as x-values increase step by step.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

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

Look at consecutive x-values and see if the corresponding y-values are getting larger. If x goes from 0→2→4 and y goes from 4→5→6, the function is increasing!

What's the difference between increasing and decreasing?

Increasing: As x gets bigger, y gets bigger too. Decreasing: As x gets bigger, y gets smaller. Think of walking uphill vs. downhill!

Can a function be increasing in some parts and decreasing in others?

Absolutely! Most functions have different behaviors in different intervals. That's why we specify the domain where it's increasing, like $x > 0$ .

Why does the answer say x > 0 instead of x < 0?

Look carefully at the table! For x > 0 (positive values): x = 0→2→4 and y = 4→5→6 (increasing). For x < 0: x = -10→-7→-3 and y = 10→8→6 (decreasing).

What if two y-values are the same?

If consecutive y-values are equal, the function is constant in that interval (neither increasing nor decreasing). Look for sections where y-values actually change.

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