Question

graph y=IxI-4....

Answer 1

Refer to the attachment

Answer 2

as evidenced by the co-ordinates of (-4,0) (0,-4) (4,0)? how to get those points mathematically? y=x-4, y=x+4? Or - what did you apply to get those co-ordinates?

Answer 3

Mathematica generated the plot with the following Plot function call:
Plot[Abs[x] - 4, {x, -5, 5}, AspectRatio -> Automatic]

The absolute value of a signed number is the number with the sign of it stripped off.
For positive numbers there is no change. The absolute value of -4 is 4.
|-4| - 4 is 4 - 4 = 0. This is the point on the negative x axis. Remember that there is a formula to calculate y given a value of |x|. That is, y = |x|-4. At x = -4 the line crosses the negative x axis because the associated y value is |-4| -4 = 4 -4 which is 0.. When x is 0 the (|0| - 4) = -4. Both lines meet at the point (0,-4)
If you did not have to contend with the absolute operator, then the line would be straight and would not change direction at (0,-4).

Answer 4

One thing I forget to stress is that in evaluating a math expression with absolute values it is probably a good idea to evaluate the absolute values first changing any negative signs inside the two vertical bars to plus, at least in your mind.

Answer 5

Brilliant! This explains it better, I appreciate your thorough response

Answer 6

Thank you and sorry for the delay. I am 76 years old and I am not able to knock out the narrative as fast as a much younger person.

Have a good day.

Answer 7

: ) You did great! It's 3:20am here, so I'm reading slow anyway ; )