Finding Decreasing Intervals: Analyzing Function Behavior on a Grid

Function Behavior with Data Table Analysis

In which domain does the function decrease?

x-210-1.58-0.560021353.5759

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the decreasing domain of the function
00:03 The function decreases when X values increase and Y values decrease
00:07 Let's observe from the table when Y values are decreasing
00:11 From here Y values start to increase - meaning not a decreasing domain
00:22 We'll deduce the decreasing domain from this
00:29 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

In which domain does the function decrease?

x-210-1.58-0.560021353.5759

2

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 wherex<0 x < 0 X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

x<0 x < 0

3

Final Answer

x<0 x<0

Key Points to Remember

Essential concepts to master this topic
  • Decreasing Function: When x increases, y decreases simultaneously
  • Analysis Method: Check adjacent x values: x = -2 to 0, y drops from 10 to 0
  • Verification: Compare all intervals: only x<0 x < 0 shows consistent decrease ✓

Common Mistakes

Avoid these frequent errors
  • Confusing decreasing with negative y-values
    Don't think decreasing means y < 0 = wrong domain! Decreasing means y gets smaller as x increases, not that y must be negative. Always compare how y changes between consecutive x-values.

Practice Quiz

Test your knowledge with interactive questions

Does the function in the graph decrease throughout?

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FAQ

Everything you need to know about this question

What's the difference between decreasing and negative values?

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Decreasing means the function goes down as you move right (x increases). Negative values just means y < 0. A function can decrease while staying positive!

How do I read the data table correctly?

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Look at the x-values on top and y-values on bottom. Follow them from left to right to see if y is getting bigger (increasing) or smaller (decreasing).

Why isn't the answer x > 0 since y increases there?

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The question asks where the function decreases, not increases! When x>0 x > 0 , y goes from 0 to 9, so it's increasing in that domain.

Can a function decrease in multiple intervals?

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Yes! Functions can have multiple decreasing intervals. Always check each section of the domain separately and list all intervals where the function decreases.

What if two y-values are the same?

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

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