To determine whether each relation is a function or not, we will apply the definition of a function: A relation is a function if every input (x-value) is associated with exactly one output (y-value).
Now, let's analyze each relation:
Relation A:
x y
4 4
4 4
5 5
5 0
7 8
10 1
- For x = 4, y = 4.
- For x = 5, there are two outputs: y = 5 and y = 0.
Since x = 5 corresponds to two different y-values, Relation A is not a function.
Relation B: (Description: Graph of a parabola opening to the left.)
- A parabola opens to the left means that for some x-values, there can be multiple corresponding y-values.
Thus, Relation B is not a function.
Relation C: Equation: \(4x + 53 = y\)
- This can be rearranged to \(y = 4x + 53\), which is a linear equation.
In a linear equation, for every x-value, there is exactly one corresponding y-value. So, Relation C is a function.
Relation D: Equation: \(y = 8x^2\)
- This is a quadratic function. For each x-value, there is exactly one corresponding y-value.
So, Relation D is also a function.
In conclusion:
- Relation A: Not a function
- Relation B: Not a function
- Relation C: Function
- Relation D: Function