Find the range of each function for the given domain.
5. f(x) = -2x + 1; {-6, -2, 0}
6. f(x) = x3 + 1; {-2, -1, 3}
5. f(x) = -2x + 1; {-6, -2, 0}
f(-6) = 12+1 =13
f(-2) = 4+1 = 5
f(0) =1
Range {1,5,13}
6. f(x) = x3 + 1; {-2, -1, 3}
f(-2) = (-2)^3+1 =-7
f(-1) = (-1)^2 +1 =0
f(3) = (3)^3 +1 = 28
Range = {-7,0,28}
Is {-6, -2, 0} supposed to represent a given domain?
To find the range of each function for the given domain, we need to substitute the values from the domain into the functions and determine the corresponding outputs.
5. For the function f(x) = -2x + 1 and the domain {-6, -2, 0}:
- Substituting -6: f(-6) = -2(-6) + 1 = 12 + 1 = 13
- Substituting -2: f(-2) = -2(-2) + 1 = 4 + 1 = 5
- Substituting 0: f(0) = -2(0) + 1 = 0 + 1 = 1
Therefore, the range of the function for the given domain {–6, –2, 0} is {13, 5, 1}.
6. For the function f(x) = x^3 + 1 and the domain {-2, -1, 3}:
- Substituting -2: f(-2) = (-2)^3 + 1 = -8 + 1 = -7
- Substituting -1: f(-1) = (-1)^3 + 1 = -1 + 1 = 0
- Substituting 3: f(3) = (3)^3 + 1 = 27 + 1 = 28
Therefore, the range of the function for the given domain {-2, -1, 3} is {-7, 0, 28}.
To find the range of a function for a given domain, we need to substitute each value in the domain into the function and determine the corresponding values, which will give us the range.
For the first function:
f(x) = -2x + 1; {-6, -2, 0}
1. Substitute -6 into the function:
f(-6) = -2(-6) + 1
f(-6) = 12 + 1
f(-6) = 13
2. Substitute -2 into the function:
f(-2) = -2(-2) + 1
f(-2) = 4 + 1
f(-2) = 5
3. Substitute 0 into the function:
f(0) = -2(0) + 1
f(0) = 0 + 1
f(0) = 1
The range of the function for the given domain {-6, -2, 0} is {13, 5, 1}.
For the second function:
f(x) = x^3 + 1; {-2, -1, 3}
1. Substitute -2 into the function:
f(-2) = (-2)^3 + 1
f(-2) = -8 + 1
f(-2) = -7
2. Substitute -1 into the function:
f(-1) = (-1)^3 + 1
f(-1) = -1 + 1
f(-1) = 0
3. Substitute 3 into the function:
f(3) = (3)^3 + 1
f(3) = 27 + 1
f(3) = 28
The range of the function for the given domain {-2, -1, 3} is {-7, 0, 28}.