How come y = I 4-x I is a function? That's the answer my book gives but when I work it out, I get: -y=4-x and

Question

y=4-x Where did I screw up?

Answer 1

the way to read this function is
y equals the absolute value of 4 minus x

for something to be a function, there can be only one unique value of y for each value of x. This, however, is not a linear function as there is a discontinuity at x=4.

Let's look at some values and then you can plot the function

x y
-1 5
0 4
1 3
2 2
3 1
4 0
5 1 Note that the absolute value forces y to be positive
6 2
7 3
8 4

and so on

This is a piecewise linear function. A way to express it is:
for x<=4 y=4-x
and
for x>=4 y=x-4
j

Answer 2

Did you try graphing the function? That may help you understand it a bit better.

Written without the absolute value notation, you would have to show a different equation for the function for different ranges of x. The absolute value symbol means that y will NEVER be a negative number. Obviously, it will be zero when x=4, but what happens on either side of that? If x<=4, then the graph will be a straight line with a slope of -1 represented by the equation y=-x+4 or -y=x-4, which you have. When x>=4, the graph of the equation will be a straight line represented the equation y=x-4, which you also have. Each equation is valid for only some numbers, namely those which give a value not less than zero.

You can look here also:
http://www.purplemath.com/modules/absolute.htm

Answer 3

when you have a funcion with the I I all the things inside pass to positive form! i think the answer is y= 4+x because the bars means the funcion multiplicate it for -1

Answer 4

whats the original problem? Theres a few things that could cause this