Question

@satellite73: I'm not asking 'what' the range is. I want to know HOW to use the vertex and the sign of "a" (which is also the slope of the right brach) to determine the range for the absolute value function.

Answer 1

ok let me try to be more clear

Answer 2

Ok.

Answer 3

if a is negative, say a = -2, then since the absolute value of anything is greater than or equal to zero, it follows that
\[-2|x|\leq 0\] is that ok?

Answer 4

So, I should put: If "a" is negative, the absolute value of anything greater than or equalo zero will folllow that?

Answer 5

and therefore if you have as in your example
\[y=-2|x-1|+4\] you know that the "vertex" is (1,4) and therefore since the first term is AT MOST 0, the whole thing is at most 4. so the second coordinate of the vertex tells you one endpoint of the range, and the fact that a is negative tells you that the range is
\[(-\infty,4]\]

Answer 6

So, I should put: If "a" is negative, the absolute value of anything greater than or equalo zero will folllow that?

Answer 7

y = -2abs(x-1)+4

Answer 8

yes
"if a is negative, then since the absolute value of anything in greater than or equal to zero, if follows that "a" times absolute value of anything is less than or equal to zero

Answer 9

and therefore the range will be all numbers less than or equal to the second coordinate of the vertex.
how was that?

Answer 10

I understand know. Thank you soooo much!!! :)

Answer 11

yw