Finding the Domain of Increase: Analyzing a Semicircular Function

Function Behavior with Semicircular Graphs

In what domain does the function increase?

000

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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 is increasing.
00:06 It increases when both the X values and Y values go up together.
00:12 Now, let's identify where the function decreases.
00:17 So, this is where the function increases.
00:21 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In what domain does the function increase?

000

2

Step-by-step solution

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

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where x<0 x < 0 , meaning the Y values are increasing.

3

Final Answer

x<0 x<0

Key Points to Remember

Essential concepts to master this topic
  • Increasing Function: Y values rise as X values move from left to right
  • Reading Graphs: Follow the curve from left side where x<0 x < 0
  • Verification: Check that function goes upward in the negative x region ✓

Common Mistakes

Avoid these frequent errors
  • Confusing increasing direction on graphs
    Don't read the graph from right to left or focus only on positive x values = wrong domain identification! This misses where the function actually increases. Always trace the curve from left to right and identify where it rises.

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 or decreasing?

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A function is increasing when both x and y values go up together as you move from left to right. If y goes down while x goes up, the function is decreasing.

Why does this semicircle increase only when x < 0?

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Looking at the left half of the semicircle, as x moves from negative values toward 0, the y values rise upward. On the right side (x > 0), the y values fall downward, so it's decreasing there.

What does 'domain of increase' mean exactly?

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The domain of increase is the set of all x-values where the function is going upward. It's the horizontal span where the graph rises as you read from left to right.

Can a function increase in multiple separate intervals?

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Yes! Many functions increase in some intervals and decrease in others. Always check each section of the graph separately to find all increasing domains.

How do I write the domain mathematically?

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Use inequality notation like x<0 x < 0 for this problem, or interval notation like (,0) (-\infty, 0) . Both show the same set of x-values.

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