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. $f(x)=y-11
Answer (1)
We have the equation x + y = 11 .
Isolate y to express it as a function of x : y = 11 − x .
Rewrite the equation as a function: f ( x ) = − x + 11 .
The correct answer is f ( x ) = − x + 11 .
Explanation
Understanding the Problem We are given the equation x + y = 11 and asked to find an equivalent function of the form f ( x ) . This means we need to express y as a function of x .
Isolating y To express y as a function of x , we need to isolate y on one side of the equation. Starting with x + y = 11 , we subtract x from both sides: x + y − x = 11 − x
y = 11 − x
Expressing as a Function Now we can write this as a function f ( x ) : f ( x ) = 11 − x
f ( x ) = − x + 11
Finding the Correct Option Comparing this with the given options, we see that option B, f ( x ) = − x + 11 , matches our result.
Examples
In real life, this type of problem can be used to model relationships between two quantities that add up to a constant. For example, if you have a budget of 11 t os p e n d o na ppl es an d banana s , w h ere x i s t h e am o u n t yo u s p e n d o na ppl es an d y i s t h e am o u n t yo u s p e n d o nbanana s , t h ee q u a t i o n x+y=11 re p rese n t s a llt h e p oss ib l eco mbina t i o n so f a ppl e an d banana s p e n d in g t ha t e x ha u s t yo u r b u d g e t . T h e f u n c t i o n f(x) = -x + 11$ then tells you how much you can spend on bananas given any amount spent on apples.
