Which one of the following equations defines y as a function of x ?
1- y=|x|+4
2- y^2=36
3- all the answers are true
4- y = ± √x
y is a function if every value of x determines a single value of y.
The equation that defines y as a function of x is option 1: y = |x| + 4.
To determine which equation defines y as a function of x, we need to understand what it means for an equation to represent a function. In a function, for every input value (x), there can only be one corresponding output value (y).
Let's analyze each of the given equations to see if they meet this criteria:
1. y = |x| + 4
This equation represents a function because for every x value, there is only one corresponding value for y. The expression |x| represents the absolute value of x, which can be positive or zero. Adding 4 to the absolute value of x will result in a unique y value for each x value.
2. y^2 = 36
This equation does not represent y as a function of x because for each x value, there are two potential y values: one positive and one negative. If we take the square root of both sides to isolate y, we would get y = ±6, indicating that y can have two different values for a single x value.
3. The statement "all the answers are true" is not an equation and does not define y as a function of x. It is a general statement without a specific relationship between x and y.
4. y = ± √x
This equation does not represent y as a function of x because the ± symbol indicates that for each x value, there are two potential y values: one positive and one negative. Therefore, it does not meet the requirement of a unique output value for each input value.
Based on the analysis, only equation 1 (y = |x| + 4) defines y as a function of x.