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 follow these steps:
Step 1: Identify the type of function we have. The given function is in the form of , which is a linear function.
Step 2: Analyze the coefficient of , known as the slope . In our function, the slope is 4.
Step 3: Understand the relationship between the slope and the rate of change. For linear functions, if the slope is positive, the function is increasing.
Since the slope is positive, it means that as increases, also increases. Consequently, the function is increasing over its entire domain.
Therefore, the function is Increasing.
Increasing
Is the function in the graph decreasing?
When the slope is positive, it means that for every unit increase in x, the y-value also increases. Think of it like walking up a hill - you're going up as you move forward!
If the slope were negative (like ), then the function would be decreasing. As x increases, y would decrease - like walking downhill.
No! The y-intercept (-2 in this case) only tells you where the line crosses the y-axis. It doesn't change the direction the line is going - that's determined entirely by the slope.
Look at the line from left to right. If it goes upward (rising), the function is increasing. If it goes downward (falling), it's decreasing. The steeper the line, the larger the absolute value of the slope.
Remember: Positive slope = going UP (increasing), Negative slope = going DOWN (decreasing). Just like the + and - signs point up and down!
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