For f(x) = -x + 8, a statement that is true include the following: D. f(x - k) = f(x) + k.
In Geometry, the translation of a graph to the right would add a number to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - k)
Conversely, the translation of a graph up would add a number to the numerical value on the y-coordinate of the pre-image:
g(x) = f(x) + k
Assuming the value of k is 1, we would evaluate the given expressions as follows;
f(x+k) = f(x) + k
f(x+1)= (-x + 8 + 1) + 1
f(x+1)= -x + 9 + 1
f(x+1)= -x + 10 (False).
f(x-k) = f(x) - k
f(x - 1) = (-x + 8 - 1) - 1
f(x - 1) = -x + 7 - 1
f(x - 1) = -x + 6 (False).
f(x+k) = f(x) + f(k)
f(x+1)= (-x + 8 + 1) + (-1 + 8)
f(x+1)= -x + 9 + 1 + 7
f(x+1)= -x + 17 (False).
f(x - k) = f(x) + k
f(x - 1) = (-x + 8 - 1) + 1
f(x - 1) = -x + 7 + 1
f(x - 1) = -x + 8 (True).
Complete Question:
For f(x) = -x + 8, which statement is true?
A. f(x+k) = f(x) + k
B. f(x-k) = f(x) - k
C. f(x+k) = f(x) + f(k)
D. f(x - k) = f(x) + k