Question

where does the function intersect the x-axis ?

y=l x-5 l

Answer 1

if i set y=0, how would i get rid of the absolute value lines ?

Answer 2

by definition function intersects the x axis at y=0

Answer 3

so you have 0=|x-5| | | function simply returns same magnitude but answers are always >=0.

Answer 4

so when inside of || = 0, it returns 0.

Answer 5

Should probably explain the x-coordinate as well, just in case :P

Answer 6

so i would set the value of "x" to positive 5 so it can equal 0 ?

Answer 7

exactly

Answer 8

so would the function intersect with the x-axis @ (0,0) ???

Answer 9

Nope.

Answer 10

(5,0)

Answer 11

There ya go.

Answer 12

because you substitute 5 for x right ?

Answer 13

Well, you normally want to solve for x. You know if you had something like 2x + 6 = 8 you would get x by itself, right?

Answer 14

yes, but in this case you are right ?

Answer 15

Well, I just want to make sure we get the concept. Well with absolute value, we just want the | | part by itself. Once we get the absolute value by itself on one side of the equation we can drop the absolute value bars. Once we drop the absolute value bars we have to write two equations. One equation makes the absolute value equal to the other side but positive, the other equation sets the absolute value equal to the other side, but negative. So with your equation, the absolute value was already by itself. Because of that, we had this:
x - 5 = 0
x - 5 = -0
Of course -0 is still 0. So then from there we would solve for x by adding 5 to both sides. This is why x = 5 and why the intercept is at (5,0)

You care if I show another example in case we get another problem that might be a little bit different?

Answer 16

oh yes i see.
no, be my guest. i might see another problem like this

Answer 17

Alright, sure. So let's say we need to find where the function intersects the x-acis, but we have this instead:
|x + 4| - 2 = 0
Now this time we actually have something outside of the absolute value bars. Now as I said above, we have to get the absolute value bars by themselves first, so I do that by adding 2 to both sides to get:
|x + 4| = 2
Now that I have the absolute value by itself, I can drop the bars. Now once I drop the bars, I have to make the other side both positive and negative. So that means I have these two equations I need to solve for:
x + 4 = 2
x + 4 = -2
So solving both of those equations:
x + 4 = 2
- 4 -4
x = -2

and

x + 4 = -2
- 4 -4
x = -6.
So I touch the x-axis at (-6, 0) and (-2, 0). Kinda make sense?

Answer 18

this makes perfect sense. thank you so much. this gave me a much more clearer perspective of how to solve these kind of equations. i really do appreciate it!(: you're awesome!!

Answer 19

Yep, np, glad it helps ^_^