Find the Increasing Domain: Analyzing f(x) Values from -2 to 5

Function Behavior with Table Analysis

In which domain is the function increasing?

f(x)x-210-1.58-0.560112133183.520526

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the domain of increase of the function
00:04 The function increases when X and Y values increase simultaneously
00:09 From this point the function begins to increase
00:21 We'll deduce from this the domain of increase
00:30 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

In which domain is the function increasing?

f(x)x-210-1.58-0.560112133183.520526

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>0.5 x > -0.5 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x>0.5 x > -0.5

3

Final Answer

x>0.5 x>-0.5

Key Points to Remember

Essential concepts to master this topic
  • Increasing Rule: Function increases when both x and y values increase together
  • Analysis Method: Compare consecutive points: (-0.5, 6) to (0, 11) shows y increases
  • Verification: Check entire domain x > -0.5 shows continuous increasing pattern ✓

Common Mistakes

Avoid these frequent errors
  • Confusing increasing intervals with individual point comparisons
    Don't just look at one pair of points like (3, 18) and (5, 26) = incomplete analysis! This misses where the function actually starts increasing. Always examine the complete pattern from the beginning of the increasing interval.

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 do I know when a function starts increasing from a table?

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Look for the turning point where the pattern changes. In this table, f(x) decreases until x = -0.5 (where f(x) = 6), then increases for all x > -0.5.

What if the function goes up and down multiple times?

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Then you'll have multiple increasing intervals! You need to identify each separate interval where the function consistently increases, not just the overall trend.

Why isn't the answer x > 0 since that's where most increases happen?

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Because the function actually starts increasing at x = -0.5, not x = 0. From (-0.5, 6) to (0, 11), f(x) increases by 5 units, so the increasing domain begins earlier.

Can I use the slope between points to check if it's increasing?

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Yes! Calculate change in ychange in x \frac{\text{change in y}}{\text{change in x}} between consecutive points. If the slope is positive, the function is increasing in that interval.

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

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Increasing: As x gets larger, f(x) gets larger too
Decreasing: As x gets larger, f(x) gets smaller
Think of it like walking uphill vs downhill!

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