Question

determine whether the following equation defines y as a function of x.
x + y = 49

does the equation x + y = 49 define y as a function of x?
yes
no

Explanation:

Step1: Recall the definition of a function

A relation defines \( y \) as a function of \( x \) if for each input \( x \), there is exactly one output \( y \).

Step2: Solve the equation for \( y \)

Starting with the equation \( x + y = 49 \), we can isolate \( y \) by subtracting \( x \) from both sides.
\[
y = 49 - x
\]

Step3: Analyze the solution

For any given value of \( x \), when we substitute it into the equation \( y = 49 - x \), we will get exactly one value of \( y \). For example, if \( x = 0 \), then \( y = 49 - 0 = 49 \); if \( x = 5 \), then \( y = 49 - 5 = 44 \), and so on. There is no value of \( x \) for which we would get more than one value of \( y \). So, this relation satisfies the definition of a function.

Answer:

Yes