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 if the function is increasing or decreasing, we analyze its slope.
Therefore, the function is Decreasing.
Decreasing
Does the function in the graph decrease throughout?
Look at the coefficient of x (the slope). If it's positive, the function is increasing. If it's negative, the function is decreasing. In , the coefficient of x is -1, so it's decreasing.
A decreasing function means that as x-values get larger, the y-values get smaller. Think of it like going downhill - as you move right on the graph, the line goes down.
No! The y-intercept (-2 in this case) only tells you where the line crosses the y-axis. It doesn't change the direction of the line. Only the slope determines if the function increases or decreases.
Look at the line from left to right. If it's going downward, the function is decreasing. If it's going upward, the function is increasing. You can also pick any two points and check if y decreases as x increases.
If the slope is zero (like ), the function is neither increasing nor decreasing - it's constant! The line is horizontal.
Yes! Pick any two points. For : when x = 0, y = -2; when x = 1, y = -3. Since y went from -2 to -3 (decreased) while x increased, the function is decreasing.
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