Find the range of each function for the given domain.
1. f(x) = -2x + 1; {-6, -2, 0}
2. f(x) = x3 + 1; {-2, -1, 3}
1.) f(x) = -2x + 1; {-6, -2, 0}
-2(-6) + 1 = 13
-2(-2) + 1 = 5
-2(0) + 1 = 1
range: {13, 5, 1}
2.) f(x) = x^3 + 1; {-2, -1 3}
-2^3 + 1 = -7
-1^3 + 1 = 0
3^3 + 1 = 28
range: {-7, 0, 28}
To find the range of each function for the given domain, we need to substitute each value from the domain into the function and determine the corresponding output values. The range is the set of all possible output values.
1. f(x) = -2x + 1; {-6, -2, 0}
Let's substitute each value from the domain into the function:
- For x = -6: f(-6) = -2(-6) + 1 = 12 + 1 = 13
- For x = -2: f(-2) = -2(-2) + 1 = 4 + 1 = 5
- For x = 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}.
2. f(x) = x^3 + 1; {-2, -1, 3}
Let's substitute each value from the domain into the function:
- For x = -2: f(-2) = (-2)^3 + 1 = -8 + 1 = -7
- For x = -1: f(-1) = (-1)^3 + 1 = -1 + 1 = 0
- For x = 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}.