Question: Lorraine writes the equation shown.
$x^2 + y - 15 = 0$
She wants to describe the equation using the term relation and the term function.
The equation represents X a relation but not a function
1. **State the problem:**
Lorraine has the equation $$x^2 + y - 15 = 0$$ and wants to describe it using the terms "relation" and "function".
2. **Rewrite the equation to express $y$ in terms of $x$:**
$$x^2 + y - 15 = 0 \implies y = 15 - x^2$$
3. **Understand the terms:**
- A **relation** is any set of ordered pairs $(x,y)$ that satisfy the equation.
- A **function** is a relation where each input $x$ corresponds to exactly one output $y$.
4. **Check if the equation represents a function:**
Since $y = 15 - x^2$, for each $x$ there is exactly one $y$ value.
5. **Conclusion:**
The equation represents both a relation and a function because it assigns exactly one $y$ for each $x$.
Lorraine's statement that it is a relation but not a function is incorrect.
**Final answer:** The equation $$x^2 + y - 15 = 0$$ represents a relation that is also a function.