Is the function in the graph decreasing?
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Is the function in the graph decreasing?
To solve this problem, we'll follow these steps:
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.
Yes
Does the function in the graph decrease throughout?
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.
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?
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.
A function is decreasing when: for any two points, if , then . In simple terms: bigger input gives smaller output.
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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