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 given function is in the standard linear form , where is the slope. For the function , the slope is .
The behavior of a linear function is determined by its slope:
In this case, since the slope , which is less than zero, the function is decreasing.
Thus, the function is decreasing.
The correct choice is choice 2: Decreasing.
Decreasing
Does the function in the graph decrease throughout?
Rewrite the equation in slope-intercept form . So becomes , making the slope m = -1.
A slope of -1 means for every 1 unit you move right on the x-axis, the line goes down 1 unit on the y-axis. It's a 45-degree downward slant!
Because the slope is negative (-1). When slope is negative, as x gets larger, y gets smaller. That's the definition of a decreasing function!
Yes! Look at the line from left to right. If it goes up, it's increasing. If it goes down, it's decreasing. This line clearly slopes downward.
Then the slope would be positive (+1), making it an increasing function. The sign of the slope is what determines increasing vs decreasing behavior.
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