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 solve this problem, we need to determine whether the linear function is increasing or decreasing.
Linear functions are represented by the equation , where is the slope. The slope indicates the rate at which the function increases or decreases as we move along the x-axis.
For the given function , the slope is 2. This is a positive number.
A positive slope indicates that as increases, also increases. Therefore, the function is increasing.
Since a positive slope in the linear function suggests an increasing nature, we can conclude that the function is growing.
Therefore, the function is Increasing.
Increasing
Is the function in the graph decreasing?
Look at the coefficient of x (the slope)! In , the coefficient is 2. Since 2 is positive, the function is increasing.
A negative slope means the function is decreasing. As x increases, y would decrease. For example, is a decreasing function.
No! The +2 is the y-intercept - it only tells you where the line crosses the y-axis. Only the slope (coefficient of x) determines if the function increases or decreases.
Absolutely! Look at the line from left to right. If it goes upward, the function is increasing. If it goes downward, it's decreasing. The graph shows an upward trend, confirming our answer.
The slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units. This constant positive change makes the function increasing.
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