Question

B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?

Answer 1

The absolute value gives always a positive number.

If a is negative, then a|x| is negative and |ax| is positive.

Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.

Another way to see it, is by using the property:

`\mleft|ax\mright|=\mleft|a\mright|\cdot\mleft|x\mright|`

Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.