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 will analyze its slope:
Step 1: Identify the function as a linear function in the form where and .
Step 2: Recall that for a linear function, if the slope , the function is increasing. Conversely, if , it is decreasing.
Step 3: Calculate the slope: . Since is positive, this means the function is increasing.
The behavior of the function depends on the sign of the slope. Here, because the slope is positive, the function increases as increases across its entire domain.
Therefore, the function is Increasing.
Increasing
Is the function in the graph decreasing?
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 is +1, so it's increasing!
No! The y-intercept only tells you where the line crosses the y-axis. It doesn't affect the direction of the line. Only the slope determines if the function increases or decreases.
If the slope is zero, the function is neither increasing nor decreasing - it's constant! The graph would be a horizontal line where y stays the same for all x values.
Look at the line from left to right. If it goes upward, it's increasing. If it goes downward, it's decreasing. The graph shows the line going up as you move from left to right!
Never! A linear function has the same slope everywhere, so it's either always increasing, always decreasing, or always constant. It can't change its behavior like curved functions do.
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