Finding Decreasing Intervals on a Curved Function Graph: [0,6] Analysis

Function Behavior with Monotonic Increasing Curves

Identify in which interval the function is decreasing?

222444666000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the domain where the function decreases
00:03 The function decreases when X values increase and Y values decrease
00:09 It seems that our function only increases
00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Identify in which interval the function is decreasing?

222444666000

2

Step-by-step solution

Let's remember that the function increases when X values and Y values increase simultaneously.

Furthermore the function decreases when X values increase and Y values decrease simultaneously.

In the given graph, we notice that the function only increases, meaning it increases for all X. Therefore we can deduce that there is no domain of decrease.

3

Final Answer

No decreasing interval

Key Points to Remember

Essential concepts to master this topic
  • Decreasing Function: As x increases, y values must decrease simultaneously
  • Visual Check: Look for downward slopes from left to right
  • Verify: Trace any section - if it only goes up, no decreasing intervals exist ✓

Common Mistakes

Avoid these frequent errors
  • Confusing increasing with decreasing direction
    Don't think a function is decreasing just because it curves or has different slopes = wrong analysis! Curves can still increase throughout. Always check if y-values actually decrease as x increases from left to right.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

How can I tell if a function is decreasing just by looking at the graph?

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Look for sections where the graph goes downward as you move from left to right. If the entire graph only goes up or stays level, there are no decreasing intervals.

What does 'monotonic increasing' mean?

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A monotonic increasing function means it never decreases - it either goes up or stays flat. Even if it curves, as long as it doesn't go down, it's still increasing!

Can a curved function still be always increasing?

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Absolutely! Curves don't mean decreasing. This graph curves upward like a smile, but it never goes down. The curve just shows it increases at different rates.

Why is the answer 'No decreasing interval' instead of a specific interval?

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Because when you trace this graph from x=0 x = 0 to x=6 x = 6 , the function only goes up. There's literally no section where y-values decrease as x increases!

What if the graph was flat somewhere - would that be decreasing?

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No! A flat (horizontal) section means the function is constant, not decreasing. For decreasing, you need the graph to actually go downward.

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