Determine whether the equation defines y as a function of x.
a) x^2 + y = 25

To determine whether the equation \( x^2 + y = 25 \) defines \( y \) as a function of \( x \), we need to express \( y \) explicitly in terms of \( x \) and check if, for each value of \( x \), there is only one corresponding value of \( y \).

Let's solve for \( y \):

\[
x^2 + y = 25
\]

Subtract \( x^2 \) from both sides:

\[
y = 25 - x^2
\]

This equation expresses \( y \) as a function of \( x \), because for every value of \( x \), there is exactly **one** corresponding value of \( y \). Therefore, the equation **does** define \( y \) as a function of \( x \).

### Summary:
Yes, the equation \( x^2 + y = 25 \) defines \( y \) as a function of \( x \).

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Would you like further details or have any questions?

Here are five related questions to explore:
1. What does the graph of \( y = 25 - x^2 \) look like?
2. How do you determine the domain and range of this function?
3. What is the vertex of the function \( y = 25 - x^2 \)?
4. Can you determine whether this function is increasing or decreasing?
5. How does the function \( y = 25 - x^2 \) relate to a circle's equation?

**Tip:** Always check if each \( x \)-value has a unique \( y \)-value to confirm if it's a valid function!

Determine whether the equation defines y as a function of x. a) x^2 + y = 25

Find out if the equation x^2 + y = 25 defines y as a function of x. This step-by-step solution explains how to express y in terms of x and verifies if each x-value has a unique y-value. Ideal for students in Grades 8-10 studying functions and quadratic equations.

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