What is the graph of the function rule? y=I5xI -2
To understand the graph of the function rule y = |5x| - 2, we can break it down into two parts. First, let's examine the function y = |x|, which represents the absolute value of x.
The absolute value of a number is always positive or zero, so |x| will never be negative. This means that the graph of y = |x| will stay above or exactly on the x-axis (y = 0).
Now, in our original function y = |5x| - 2, the absolute value is applied to 5x. This means that the value inside the absolute value brackets, 5x, can be either positive or negative.
If 5x is positive, then |5x| = 5x. If 5x is negative, then |5x| = -5x. So we have two different cases to consider.
1. When 5x is positive (5x > 0):
In this case, the function y = |5x| - 2 simplifies to y = 5x - 2. Here, the graph of y = 5x - 2 will stay above or exactly on the x-axis (y = 0), just like y = |x|.
2. When 5x is negative (5x < 0):
In this case, the function y = |5x| - 2 simplifies to y = -5x - 2. Here, the graph of y = -5x - 2 will also stay above or exactly on the x-axis (y = 0).
Combining both cases, we can conclude that the graph of y = |5x| - 2 will be above or exactly on the x-axis for all x-values. It will be a continuous line without any breaks, and it will shift down by 2 units compared to the graph of y = |x|.
In summary, the graph of the function rule y = |5x| - 2 will be a continuous line that remains above or exactly on the x-axis, shifted down by 2 units.