Question

select the correct answer. which function has the same graph as ( x + y = 11 )? a. ( f(x) = -y + 11 ) b. ( f(x) = -x + 11 ) c. ( f(x) = x - 11 ) d. ( f(x) = y - 11 )

Explanation:

Step1: Start with the given equation

We have the equation \( x + y = 11 \). We need to express this in the form of a function \( f(x) \), which is typically \( y = f(x) \). So we solve for \( y \) in terms of \( x \).

Step2: Solve for \( y \)

Subtract \( x \) from both sides of the equation \( x + y = 11 \).
\[

$$\begin{align*} x + y - x &= 11 - x\\ y &= -x + 11 \end{align*}$$

\]
Since \( f(x)=y \), we can write \( f(x)= -x + 11 \).

Answer:

B. \( f(x) = -x + 11 \)