Determine the Domain of Increasing Behavior in a Curved Function Graph

Function Behavior with Graphical Analysis

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

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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 A function increases when, as X values go up, Y values also go up.
00:11 For this function, it looks like it keeps increasing the whole time.
00:16 And that's how we solve this problem!

Step-by-step written solution

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1

Understand the problem

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

2

Step-by-step solution

Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.

3

Final Answer

All values of x x

Key Points to Remember

Essential concepts to master this topic
  • Increasing Function: Y-values rise as X-values move from left to right
  • Visual Check: Trace the curve - does it go upward everywhere?
  • Domain Verification: Check every section of the graph for upward movement ✓

Common Mistakes

Avoid these frequent errors
  • Only checking part of the graph
    Don't just look at one section and assume the whole function behaves the same way = missing decreasing intervals! You might identify only x > 0 as increasing when actually the entire domain is increasing. Always trace the entire visible curve from left to right to check all intervals.

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 can I tell if a function is increasing just by looking at the graph?

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Follow the curve with your finger from left to right. If the curve consistently moves upward (even if it curves), then it's increasing in that interval.

What if the graph has flat horizontal sections?

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Horizontal sections are neither increasing nor decreasing - they're constant. In this problem, the curve continuously rises, so there are no flat sections.

Can a function increase in some parts and decrease in others?

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Absolutely! Many functions have different behaviors in different intervals. That's why we specify the domain where the function is increasing.

Why does this curve increase everywhere when it looks like it's curving?

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The curve bends, but it never goes downward. Even when curving, as long as the Y-values keep getting larger as X increases, the function is still increasing.

What would a decreasing function look like on this same graph?

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A decreasing function would slope downward from left to right. The Y-values would get smaller as the X-values get larger.

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