We have the function:
y = |x|
And its graph (in blue):
From this graph, we see that:
y = 1 |x| opens upwards
We know that if we multiply a function by a constant non-zero (and positive) factor, it shrinks or expands horizontally. If this factor is less than 1, then it expands; otherwise, it shrinks. For the function:
y = |x|/3
We see that 1/3 < 1, so its graph is wider than the |x| function.
Now, for y = 3|x|, we see that 3 > 1, so its graph is narrower than |x|.
But if we multiply by a negative number, the function expands or shrinks and, additionally, it is reflected with respect to the x-axis. For the function y = -|x|/2, we see that it expands and gets reflected.
Summarizing:
y = |x| opens upwards
y = |x|/3 opens upwards and is the widest
y = 3|x| opens upwards and is the narrowest
y = -|x|/2 opens downwards
