Function Domain Analysis: Finding Increasing Intervals from Value Table

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

Look at consecutive points and see if the y-values go up as the x-values go up. If f(1)

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

Increasing: y-values get larger as x gets larger (going uphill). Decreasing: y-values get smaller as x gets larger (going downhill).

Q: Why does the function stop being increasing at x=3?

At x=3, f(3)=5, but at x=4, f(4)=3. Since 5 > 3, the y-values start decreasing after x=3, so the increasing interval ends there.

Q: Can a function be both increasing and decreasing?

Yes, but in different intervals! A function can increase from x=0 to x=3, then decrease from x=3 to x=7. We describe behavior over specific domains.

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

If f(2) = f(3), the function is constant (flat) between those points. It's neither increasing nor decreasing in that small interval.

Function Behavior with Value Tables

In which domain is the function increasing?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the domain of increase of the function

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

00:11 At this point the function starts to decrease

00:21 From this we'll deduce the domain of increase

00:29 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

In which domain is the function increasing?

Step-by-step solution

Note 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 $x < 3$ the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x < 3$

Final Answer

$x<3$

Key Points to Remember

Essential concepts to master this topic

Increasing Function: Both x-values and y-values increase together simultaneously
Technique: Compare consecutive points: (0,0), (1,2), (2,3), (3,5) all increase
Check: Verify y-values rise as x increases: 0→2→3→5 confirms increasing ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing intervals with decreasing ones
Don't look at where y-values are largest like x=3 with f(3)=5 = wrong interval! This identifies maximum points, not increasing behavior. Always compare how y-values change as x increases 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 points and see if the y-values go up as the x-values go up. If f(1) < f(2) < f(3), then the function is increasing from x=1 to x=3!

What's the difference between increasing and decreasing?

Increasing: y-values get larger as x gets larger (going uphill). Decreasing: y-values get smaller as x gets larger (going downhill).

Why does the function stop being increasing at x=3?

At x=3, f(3)=5, but at x=4, f(4)=3. Since 5 > 3, the y-values start decreasing after x=3, so the increasing interval ends there.

Can a function be both increasing and decreasing?

Yes, but in different intervals! A function can increase from x=0 to x=3, then decrease from x=3 to x=7. We describe behavior over specific domains.

What if two consecutive y-values are the same?

If f(2) = f(3), the function is constant (flat) between those points. It's neither increasing nor decreasing in that small interval.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime