which of the following relationships is a function
a.Domain Range B.y^2=x^2-3x+4
3 2
4 1
7
c.Domain Range C.y^2=2x^2
13 0
2 4
-1
To determine if a relationship is a function, we need to ensure that each input (value in the domain) is associated with only one output (value in the range).
Let's analyze each relationship:
A. y^2 = x^2 - 3x + 4
For each input value in the domain, does it yield a unique output value in the range? Let's find out.
For y = 3, we substitute this value into the equation:
3^2 = x^2 - 3x + 4
9 = x^2 - 3x + 4
0 = x^2 - 3x - 5
By solving this quadratic equation, we obtain two possible values for x: x ≈ -1.236 and x ≈ 4.236.
Since the input value y = 3 has two possible output values, the relationship in A is NOT a function.
B. y^2 = 2x^2
Again, we'll verify if each input in the domain has a unique output in the range.
For y = 13, we substitute this value into the equation:
13^2 = 2x^2
169 = 2x^2
Solving for x, we find x = ± √(169/2) ≈ ± 8.703.
Since the input value y = 13 has two possible output values, the relationship in C is NOT a function.
C. The given relationship does not specify any equation, so it cannot be evaluated.
Among the given options, none of the relationships are functions since they do not satisfy the criterion of having each input value associated with only one output value.