Finding Function Increase Domain with Vertical Line x=-0.8: Graph Analysis

Function Analysis with Increasing Intervals

In which domain does the function increase?

Green line:
x=0.8 x=-0.8

–2–2–2222222000

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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 It appears that the function always increases
00:13 And this is 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 does the function increase?

Green line:
x=0.8 x=-0.8

–2–2–2222222000

2

Step-by-step solution

The function increases if X values and Y values increase simultaneously.
In this function, despite its unusual form, we can observe that the function continues to increase according to the definition at all times,
Furthermore there is no stage where the function decreases.
Therefore, we can say that the function increases for all X, there is no X we can input where the function will be decreasing.

3

Final Answer

All values of x x

Key Points to Remember

Essential concepts to master this topic
  • Definition: Function increases when both x and y values rise together
  • Graph Reading: Follow curve from left to right - always moving upward
  • Verification: Check entire graph shows no downward slopes anywhere ✓

Common Mistakes

Avoid these frequent errors
  • Confusing local behavior with global behavior
    Don't focus only on steep parts or assume the green line at x = -0.8 creates a boundary! This ignores the complete function behavior. Always examine the entire curve from left to right to determine where the function consistently increases.

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

What does the green line at x = -0.8 represent?

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The green vertical line at x=0.8 x = -0.8 is just a reference marker. It doesn't affect whether the function is increasing - it's simply showing a specific x-value on the graph.

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

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Move your eyes from left to right along the curve. If the function consistently goes upward (or stays level), it's increasing. If it ever goes downward, it's decreasing in that interval.

Can a function increase everywhere?

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Yes! Some functions increase for all real values of x. This means no matter what x-value you choose, the function keeps rising as x gets larger.

What if the function looks flat in some places?

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If a function is flat (horizontal), it's neither increasing nor decreasing - it's constant. But if it never goes downward anywhere, we can still say it's non-decreasing overall.

Why isn't the answer 'x > 0' or 'x > -0.8'?

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Looking at the graph, the function increases everywhere - both before and after x = 0 and x = -0.8. There's no point where it starts decreasing, so the domain is all real numbers.

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