Function Analysis: Finding Increasing Intervals in Domain [-2, 5]

Function Behavior with Table Analysis

In which domain is the function increasing?

f(x)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
00:03 Let's find where the function increases.
00:06 The function grows when both X and Y values grow together.
00:15 From this point, the function starts to increase.
00:23 We can determine from this where the function is increasing.
00:30 And that's how we find 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 is the function increasing?

f(x)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 the X values and Y values increase simultaneously.

Therefore, the function increases 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
  • Increasing Function: Both x-values and y-values increase together simultaneously
  • Table Reading: Compare consecutive points: x = 0 to x = 2 gives y = 0 to y = 1
  • Verification: Check all intervals: x > 0 shows consistent upward pattern ✓

Common Mistakes

Avoid these frequent errors
  • Looking at isolated points instead of intervals
    Don't just compare two random points like x = -2 and x = 3 = misleading conclusion! This ignores what happens between points and can miss where the function actually changes direction. Always examine consecutive intervals to see the true behavior pattern.

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 tell if a function is increasing from a table?

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Look at consecutive x-values in order. If the y-values get larger as x gets larger, the function is increasing in that interval. Check each pair systematically!

What does 'x > 0' mean as an answer?

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It means the function is increasing for all x-values greater than 0 within the given domain. So from x = 0 onwards, the function keeps going up.

Why isn't the answer 'x < 2' when the function goes up until x = 2?

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Because the function continues increasing after x = 2! Look at the table: from x = 2 to x = 3, y goes from 1 to 5, and from x = 3 to x = 5, y goes from 5 to 9.

Do I need to check every single point?

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Not every point, but check consecutive intervals. Look at each pair of neighboring x-values to see if y increases, decreases, or stays the same.

What if the function increases in some parts but not others?

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Then you need to identify specific intervals where it increases. A function can increase in one part of its domain and decrease in another - that's totally normal!

Can a function be increasing at just one point?

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No! Increasing or decreasing describes behavior over an interval (range of x-values), not at individual points. You need at least two points to compare.

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