Determine whether the equation represents y as a function of x.
|y| = 4 - x
If I plug in 5, then I get -1, but it also means 1. Does that mean y has 2 values which means that it is not a function?
You are correct.
There are two y's for each x. y is not a function of x.
To determine whether the equation represents y as a function of x, we need to check if each value of x corresponds to only one value of y.
In this case, the equation is |y| = 4 - x. The absolute value function |y| means that y can take on positive or negative values.
Let's go through a step-by-step process to determine if the equation represents y as a function of x:
1. Identify the absolute value expression: |y|
2. Set up two separate equations: y = 4 - x and y = -(4 - x) (when taking the positive or negative value of y)
3. Simplify both equations individually:
a) y = 4 - x (positive value)
b) y = -4 + x (negative value)
Now, we can see that the equation represents y as a function of x since for each given value of x, either y = 4 - x or y = -4 + x.
Let's take the example you mentioned, plugging in x = 5:
1. For y = 4 - x:
y = 4 - 5
y = -1
2. For y = -4 + x:
y = -4 + 5
y = 1
So, when x = 5, we get two different values for y: -1 and 1. This means that y does indeed have two different values, indicating that the equation does not represent y as a function of x.
In conclusion, the given equation, |y| = 4 - x, does not represent y as a function of x because it produces multiple values of y for certain values of x.