How do you check the solutions of absolute value functions by graphing????

[brandoncasilla]

Ok so the absolute value is |x-4|=10

I know that you have to take the opposite for the y intercept so its has a y int. of 4 and the x is also a 4

Then graph the function and it should have a v shape.

The part I'm stuck on is the 10 do I take the opposite or do I take it as a positive??

 

[daon2]

Graph y=|x-4| (the "v-function" you described) and y=10 (the horizontal line with y-intercept 10) on the same axes, and look at where they intersect. The x values of the points of intersection is the solution.

 

[DrPhil]

The part I'm stuck on is the 10 do I take the opposite or do I take it as a positive??

The 10 is exactly as written - positive. There is no reason to change its sign.

 

[HallsofIvy]

Ok so the absolute value is |x-4|=10

I know that you have to take the opposite for the y intercept so its has a y int. of 4 and the x is also a 4

The y intercept of what? If you are referring to y= |x- 4|, yes, when x= 0, y= |0- 4|= 4.

Then graph the function and it should have a v shape. [/quote]
Graph what function? You have an equation but no specific function. You could interpret that equation as either f(x)= |x- 4|= 10 or as f(x)= |x- 4|- 10= 0. You seem, above, to be assuming f(x)= |x- 4|.

The part I'm stuck on is the 10 do I take the opposite or do I take it as a positive??

What was the exact wording of the question? It really makes no sense to give an equation and then start talking about graphing a "function". If your purpose is to show the solutions on the graph, graph both y= |x- 4| and y= 10. The solutions are where those two graphs cross. Or, interpreting "the function" to be f(x)= |x- 4|- 10= 0, you will have a line going down to the right, to (4, -10), the back up. The solutions to f(x)= |x- 4|- 10= 0 are where that graph crosses the x axis, y= 0.