Function Table Analysis: Finding Increasing Intervals from -4 to 14

Function Behavior with Table Data

In which domain is the function increasing?

f(x)x-44-1100116210014-78-9

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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.
00:06 The function goes up when both X and Y values increase together.
00:13 Here, you'll see the function start to rise.
00:19 But at this point, the function starts to go down again.
00:26 So, we can deduce the domain where the function increases.
00:35 And there you go! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In which domain is the function increasing?

f(x)x-44-1100116210014-78-9

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 where10>x>0 10 > x > 0 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

10>x>0 10 > x > 0

3

Final Answer

10>x>0 10 > x > 0

Key Points to Remember

Essential concepts to master this topic
  • Increasing Function: Function values rise as x-values increase from left to right
  • Technique: Compare consecutive points: from x=0 to x=6, f(x) goes 0→1→2
  • Check: Verify all intervals: decreasing from x=-4 to x=0, then increasing from x=0 to x=10 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing x and f(x) values when analyzing trends
    Don't look at just the f(x) values going up or down = ignoring the x direction! A function increases only when BOTH x increases AND f(x) increases together. Always compare points moving from left to right on the x-axis.

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

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

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Look at consecutive x-values from left to right. If the f(x) values get larger as x gets larger, the function is increasing in that interval.

Why isn't the function increasing everywhere?

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From the table, you can see that from x=-4 to x=0, the f(x) values go down (4→1→0), so the function is decreasing in that interval.

What does the notation 10 > x > 0 mean?

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This means x is between 0 and 10. It's the same as writing 0<x<10 0 < x < 10 . Both notations describe the interval where the function increases.

Can a function be both increasing and decreasing?

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Yes! A function can increase in some intervals and decrease in others. That's exactly what happens here - it decreases from x=-4 to x=0, then increases from x=0 to x=10.

What happens after x=10 in this table?

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After x=10, the function starts decreasing again. At x=10, f(x)=0, then at x=14, f(x)=-7, showing the function values are getting smaller.

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