Analyze Function Behavior: Is y=3 Increasing, Decreasing, or Constant?

Function Behavior with Horizontal Lines

Below is a graph of a function.


Is the function increasing, decreasing, or constant?

111222333444555666777888999101010111111121212111222333444555666000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether the function is increasing, decreasing, or constant?
00:03 For this, let's take several points on the graph and observe the rate of change
00:17 We can see there's no change in Y values, therefore the function is constant
00:21 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

Below is a graph of a function.


Is the function increasing, decreasing, or constant?

111222333444555666777888999101010111111121212111222333444555666000

2

Step-by-step solution

The problem presents us with a graph of a function, and we need to determine if the function is increasing, decreasing, or constant. An increasing function would show a line rising as you move from left to right, while a decreasing function would show a line falling. A constant function would be represented by a horizontal line on the graph.

Upon examining the graph provided, we observe that the line is horizontal. This means that the y-value of the function does not change regardless of the x-value. The horizontal nature of the line indicates that the function’s output remains the same across its domain, implying that there is neither an upward nor downward trend.

In this scenario, where the graphical line does not incline or decline, the function is determined to be constant. Thus, the correct answer for this problem, based on the graphical representation, is that the function is constant.

Therefore, the solution to the problem is the function is constant.

3

Final Answer

Constant

Key Points to Remember

Essential concepts to master this topic
  • Definition: Constant functions have identical y-values for all x-values
  • Visual Clue: Horizontal line on graph means y=3 y = 3 throughout
  • Check: Pick any two points: both have y-coordinate of 3 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope direction with function behavior
    Don't think a line going left-to-right means increasing = wrong classification! The direction you read doesn't matter - only whether the line goes up, down, or stays level. Always look at the y-values: if they stay the same, the function is constant.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

FAQ

Everything you need to know about this question

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

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Look for a perfectly horizontal line! If the line doesn't go up or down at all, the function is constant. The y-value stays the same no matter what x-value you choose.

What does it mean when we say y = 3?

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It means that no matter what x-value you input, the output is always 3. Whether x = 1, x = 5, or x = 100, you always get y = 3!

Can a function be increasing in some parts and constant in others?

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Yes! Functions can have different behaviors in different sections. But this particular graph shows a completely horizontal line, so it's constant everywhere we can see.

Why isn't this function increasing if I read the graph from left to right?

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Reading direction doesn't determine function behavior! Increasing means the y-values get bigger as x increases. Here, all y-values equal 3, so there's no increase.

How do I check my answer?

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Pick any two different x-values from the graph and check their y-coordinates. If they're the same (like both being 3), then the function is constant

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