Graph Analysis: Identifying a Decreasing Function from Linear Plot

Function Behavior with Slope Interpretation

Is the function in the graph decreasing? yx

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Step-by-step written solution

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1

Understand the problem

Is the function in the graph decreasing? yx

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Verify the graph's overall path direction
  • Step 2: Confirm if the y-values are decreasing as we proceed from the left side of the graph to the right side (increasing x-values).

Now, let's work through each step:

Step 1: By examining the graph, the red line starts at a higher point on the y-axis and moves downward to a lower point as it moves horizontally across the x-axis from left to right.

Step 2: Since for every point, the red line descends as it progresses from the leftmost point to the rightmost, this indicates a consistent decrease in the y-values.

Therefore, the solution to the problem is Yes, the function in the graph is decreasing.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Decreasing Rule: Function decreases when y-values drop as x-values increase
  • Visual Analysis: Red line slopes downward from left to right
  • Verification: Pick two points: left point higher than right point ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the direction of the slope
    Don't look at the line going up from bottom-left to top-right and think it's increasing = wrong interpretation! The line appears to go up because of the graph orientation, but what matters is: as you move right (increasing x), does y go down? Always follow the x-direction from left to right to determine if y-values are increasing or decreasing.

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 do I tell if a function is increasing or decreasing from a graph?

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Follow the left-to-right rule: Start at the leftmost point and trace the line toward the right. If the line goes downward as you move right, it's decreasing. If it goes upward, it's increasing.

What if the line looks like it's going upward on the graph?

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Be careful about visual tricks! The line might appear to go 'up' on your screen, but what matters is the direction relative to the x-axis. Always check: as x increases (moving right), do the y-values get smaller or larger?

Can I use specific points to check if a function is decreasing?

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Yes! Pick any two points on the line. If the point with the larger x-value has a smaller y-value, then the function is decreasing between those points.

What does 'decreasing function' actually mean in math terms?

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A function is decreasing when: for any two points, if x1<x2 x_1 < x_2 , then f(x1)>f(x2) f(x_1) > f(x_2) . In simple terms: bigger input gives smaller output.

Is this the same as having a negative slope?

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For linear functions (straight lines), yes! A decreasing linear function always has a negative slope. The steeper the downward slant, the more negative the slope.

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