is y=1/2|x-2|-6 a fuction

Question

i need help with this question because mt friends are no help

Answer 1

What is the definition of a function? For each x there is one and only one 5. So for your equation:

y = 1/2 (x-2) - 6 this is indeed true. Take any x, say x = 4, Then y = 1/2 ( 4-2) - 6 = -5 one value.

This is not true for the equation of a circle centered at the origin with radius =3 given by:

x² + y² = 9 When x = 3, y = +3 or -3 Two values of y for one value of x. You can also

use the vertical line test. For a function, a vertical line drawn through a graph of the function will

intersect the graph at only one point.

Answer 2

Function: A special relationship where each input has a single output.

this is a function because for each input there is only one output. when x=2, y=-6.

Answer 3

Hello Heaven!

Yes this is a function! Why, if you do the vertical line test on it. If you graph the function you will see it have a "V" shape due to the absolute value part of its function. If you were to take a pencil and move everywhere along the function with the pencil vertical (up and down) nowhere does the function cross the pencil more than one time. In other words there is a unique correspondence of X and Y values. Therefore its a function!