Question

Four relations are shown.

Relation A

x y
4 4
4 4
5 5
5 0
7 8
10 1
Relation B
(Graph of a parabola opening to the left.)

Relation C
4x + 53 = y

Relation D
y = 8x^2

Drag the name of each relation to identify whether the relation is a function or not a function.

Answer 1

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