The equation x + y = 11 is equivalent to the function f(x) = -x + 11, making option B the correct choice. This function shares the same graph, representing the given line in the xy-plane.
The given equation x + y = 11 can be rearranged into slope-intercept form y = -x + 11, where the coefficient of x is the slope, and the constant term is the y-intercept. Comparing this with the given options:
A. f(x) = -y + 11 has a different slope (-1 instead of -1) and a different structure.
B. f(x) = -x + 11 matches the equation x + y = 11 and represents the same line in the xy-plane.
C. f(x) = x - 11 has a different slope (1 instead of -1) and a different structure.
D. f(x) = y - 11 has a different slope (1 instead of -1) and a different structure.
Therefore, the function that has the same graph as x + y = 11 is option B: f(x) = -x + 11.
The probable question may be:
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