how do u graph absolute value functions?

Question

Graph this absolute value function:

y= 3 l x-4 l - 2

how would i go about doing that?

Answer 1

THe basic absolute function is a V shape and the standard form is:
y = a|x-p|+q where (p,q) is the vertex.

For the one you have: The vertex is (4,-2). Plot this point and then follow the pattern to plot other points: Right 1, Up 3, Right 1, Up 3, etc
Do the same thing on the other side of the vertex, ie,.Left 1 Up 3, etc.

Connect the points and put arrows on the end!
Don't forget to label the function with its equation.

Answer 2

First of all, find out when the term in the absolute value sign is >= 0, and when it is < 0. Here x - 4 >= 0 when x >=4 and less than 0 other wise. Now set up the equation, for each possibility. Here we have two: x < 4, x >= 4.

If x < 4, then the absolute value of |x -4| will be positive and x -4 is negative, so the absolute value will be -(x -4) or 4 - x. So y = 3(4 -x) - 2 = 12 - 3x -2 = -3x +10. y = -3x + 10, -infinity< x < 4.
Graph this line from the beginning till x = 4.

Next if x >= 4, then the absolute value of (x -4) will be (x - 4) and y = 3(x - 4) -2 = 3x - 12 - 2 = 3x- 14. y = 3x -14, 4 <= x < infinity.

Graph this line but start at x equals 4, where the other line ended.

Answer 3

Graph two lines (rays, actually): one for when x-4 is negative, and one for when it's positive. The "bend" will be where x-4 is zero. As an example, there's the plain old absolute value function: y = |x|. Here, the graph looks like y = -x where x is negative and like y = x where x is positive, and the "bend" is where x = 0: this produces y = |0| = 0, so the bend of y = |x| is at (0,0).

Answer 4

Basically the graph is going to turn out like a v. and the function within the the bars ur supoosed to do that twice. re write the function, once making the value within the bars positive and the other making the value negative. then u figure out the values of the function.

Answer 5

The absolute linear function always has "v" shape or upside down of "v" shape. You only need to find the vertex and pick one more point to graph it.

Here are the steps you can go:

First, you graph the vertex at (4, -2).

Pick another point (3,1). ( It can be any other point.)

Now graph a line starting from the vertex (4,-2) and passing (3,1).

Graph the symmetric axis x = 4.

By symmetry, you graph another half. Then you done.

Got it?

Answer 6

|a| = a if a >= 0 AND |a| = -a of a < 0 This really is how you need to begin to think about absolute value problems and it will make them much easier for you. Just consider them 2 problems in one from the start. |3x+2| = 3x+2 when 3x+2 >= 0 So let's deal with the restriction 3x+2 >= 0 3x >= -2 x >= -2/3 So |3x+2| = 3x+2 when x >= -2/3 {I hope you can see kind of how this works} We still have a second part though. |3x+2| = -(3x+2) when 3x+2 < 0 So deal with the restriction again 3x+2 < 0 3x < -2 x < -2/3 so |3x+2| = -(3x+2) when x < -2/3 Now you have 2 different subdomains and 1 function for each of those. |3x+2| = 3x+2 when x >= -2/3 AND -(3x+2) when x < -2/3 Just always think of absolute value functions as piecewise like this and you will do fine. I have included a link to a khan academy video tutorial to help.