Given the following function:
Is the function increasing or decreasing?
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Given the following function:
Is the function increasing or decreasing?
To determine whether the function is increasing or decreasing, we need to examine its slope. The function is in the form , where is the slope.
For the given function, the slope .
Since the slope is positive, the function is increasing.
Therefore, the function is increasing.
Increasing
Is the function in the graph decreasing?
A positive slope means that as x gets larger, y also gets larger! Think of it like climbing uphill - you're moving up as you go forward.
If the slope were negative (like -3), then the function would be decreasing. As x increases, y would decrease, like going downhill.
No! The y-intercept only tells you where the line crosses the y-axis. Only the slope determines if the function increases, decreases, or stays constant.
Pick any two x-values and calculate their y-values. For example: when x = 0, . When x = 1, . Since y increased from -1 to 2, the function is increasing!
Slope = 3 means for every 1 unit you move right (increase x by 1), you move up 3 units (y increases by 3). This constant upward movement is what makes the function increasing.
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