Answer :
To determine which of the given ordered pairs is a solution to the function [tex]\( f(x) = 3x - 1 \)[/tex], we need to evaluate the function for each given [tex]\( x \)[/tex] value and see if the resulting [tex]\( y \)[/tex] value matches the [tex]\( y \)[/tex] value in the ordered pair.
Let's analyze each option:
### Option A: [tex]\((-1, 4)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = 4 \)[/tex].
Hence, [tex]\((-1, 4)\)[/tex] is not a solution.
### Option B: [tex]\((-1, -3)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = -3 \)[/tex].
Hence, [tex]\((-1, -3)\)[/tex] is not a solution.
### Option C: [tex]\((-1, -4)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which matches [tex]\( y = -4 \)[/tex].
Hence, [tex]\((-1, -4)\)[/tex] is a solution.
### Option D: [tex]\((-1, 2)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = 2 \)[/tex].
Hence, [tex]\((-1, 2)\)[/tex] is not a solution.
Therefore, the ordered pair that is a solution to the function [tex]\( f(x) = 3x - 1 \)[/tex] is:
[tex]\[ \boxed{(-1, -4)} \][/tex]
Let's analyze each option:
### Option A: [tex]\((-1, 4)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = 4 \)[/tex].
Hence, [tex]\((-1, 4)\)[/tex] is not a solution.
### Option B: [tex]\((-1, -3)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = -3 \)[/tex].
Hence, [tex]\((-1, -3)\)[/tex] is not a solution.
### Option C: [tex]\((-1, -4)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which matches [tex]\( y = -4 \)[/tex].
Hence, [tex]\((-1, -4)\)[/tex] is a solution.
### Option D: [tex]\((-1, 2)\)[/tex]
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-1) = 3(-1) - 1 = -3 - 1 = -4 \][/tex]
2. The resulting value is [tex]\( f(-1) = -4 \)[/tex], which does not match [tex]\( y = 2 \)[/tex].
Hence, [tex]\((-1, 2)\)[/tex] is not a solution.
Therefore, the ordered pair that is a solution to the function [tex]\( f(x) = 3x - 1 \)[/tex] is:
[tex]\[ \boxed{(-1, -4)} \][/tex]
