True or False: When the graph of a function is below the x-axis, it is decreasing.
Please explain the answer.
What is the function? What does the graph look like?
Clearly false.
Consider y = x
False.
The statement "When the graph of a function is below the x-axis, it is decreasing" is not always true. The position of a function relative to the x-axis does not determine whether the function is increasing or decreasing.
To determine whether a function is increasing or decreasing, you need to examine its rate of change.
In general, a function is considered decreasing if its values are getting smaller as you move from left to right along the x-axis. This means that the slope of the function, referred to as the derivative, is negative.
If a function is located below the x-axis, it means that its y-values are negative. However, it does not provide any information about the function's rate of change or whether it is increasing or decreasing.
To determine if a function is increasing or decreasing, you need to analyze the function's derivative or examine the intervals of the function where the derivative is positive (increasing) or negative (decreasing). Simply looking at the position of the graph relative to the x-axis is not sufficient to determine the direction of the function's change.