The domain of f(x)=−x+11 is {−9,−4, 0, 2, 7}.
The range of f(x) is
Responses
A. {-1, 11, 19, 30, 35}
{-1, 11, 19, 30, 35}
B. {7, 8, 9, 19, 26}
{7, 8, 9, 19, 26}
C. {4, 9, 11, 15, 20}
{4, 9, 11, 15, 20}
D. {-3, 3, 4, 9, 13}
To find the range of the function f(x), we need to substitute each value from the domain into the function and evaluate it.
Substituting -9:
f(-9) = -(-9) + 11 = 9 + 11 = 20
Substituting -4:
f(-4) = -(-4) + 11 = 4 + 11 = 15
Substituting 0:
f(0) = -(0) + 11 = 11
Substituting 2:
f(2) = -(2) + 11 = 9
Substituting 7:
f(7) = -(7) + 11 = 4
The range of f(x) is {20, 15, 11, 9, 4}, which corresponds to option C: {4, 9, 11, 15, 20}.
To find the range of the function f(x) = -x + 11, we need to evaluate the function at each value in the domain.
Given domain: {-9, -4, 0, 2, 7}
Plug in each value into the function:
f(-9) = -(-9) + 11 = 9 + 11 = 20
f(-4) = -(-4) + 11 = 4 + 11 = 15
f(0) = -(0) + 11 = 0 + 11 = 11
f(2) = -(2) + 11 = -2 + 11 = 9
f(7) = -(7) + 11 = -7 + 11 = 4
The range of f(x) is {20, 15, 11, 9, 4}.
Among the given options, the range that matches is:
C. {4, 9, 11, 15, 20}
To find the range of a function, we need to determine the set of all possible output values. In this case, the function is f(x) = -x + 11.
To find the range, we substitute each value from the domain {-9, -4, 0, 2, 7} into the function and compute the corresponding output.
1. For x = -9: f(-9) = -(-9) + 11 = 9 + 11 = 20
2. For x = -4: f(-4) = -(-4) + 11 = 4 + 11 = 15
3. For x = 0: f(0) = -(0) + 11 = 0 + 11 = 11
4. For x = 2: f(2) = -(2) + 11 = -2 + 11 = 9
5. For x = 7: f(7) = -(7) + 11 = -7 + 11 = 4
Therefore, the range of f(x) is {20, 15, 11, 9, 4}.
Comparing this result to the provided options:
A. {-1, 11, 19, 30, 35} - not a match
B. {7, 8, 9, 19, 26} - not a match
C. {4, 9, 11, 15, 20} - a match
D. {-3, 3, 4, 9, 13} - not a match
So, the correct answer is C. {4, 9, 11, 15, 20}.