Answer :
To determine which equation is true based on the given function \(f(x)\), we need to analyze each ordered pair and verify the corresponding equations. Let's carefully evaluate each one.
Given the set of ordered pairs: \(\{(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)\}\):
1. Checking \(f(-10) = 1\):
- The pair \((-10, 2)\) tells us that \(f(-10) = 2\).
- Therefore, \(f(-10) = 1\) is false.
2. Checking \(f(2) = -10\):
- The given pairs do not include any with \(2\) as the first element (input value \(x\)).
- Therefore, \(f(2) = -10\) is false (since \(f(2)\) is not defined by the given pairs anyway).
3. Checking \(f(0) = 6\):
- The pair \((0, 6)\) tells us that \(f(0) = 6\).
- Therefore, \(f(0) = 6\) is true.
4. Checking \(f(1) = -10\):
- The pair \((1, 0)\) tells us that \(f(1) = 0\).
- Therefore, \(f(1) = -10\) is false.
Based on this evaluation:
- \(f(-10) = 1\) is false.
- \(f(2) = -10\) is false.
- \(f(0) = 6\) is true.
- \(f(1) = -10\) is false.
The true equation among the provided options is:
[tex]\[ f(0) = 6 \][/tex]
Given the set of ordered pairs: \(\{(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)\}\):
1. Checking \(f(-10) = 1\):
- The pair \((-10, 2)\) tells us that \(f(-10) = 2\).
- Therefore, \(f(-10) = 1\) is false.
2. Checking \(f(2) = -10\):
- The given pairs do not include any with \(2\) as the first element (input value \(x\)).
- Therefore, \(f(2) = -10\) is false (since \(f(2)\) is not defined by the given pairs anyway).
3. Checking \(f(0) = 6\):
- The pair \((0, 6)\) tells us that \(f(0) = 6\).
- Therefore, \(f(0) = 6\) is true.
4. Checking \(f(1) = -10\):
- The pair \((1, 0)\) tells us that \(f(1) = 0\).
- Therefore, \(f(1) = -10\) is false.
Based on this evaluation:
- \(f(-10) = 1\) is false.
- \(f(2) = -10\) is false.
- \(f(0) = 6\) is true.
- \(f(1) = -10\) is false.
The true equation among the provided options is:
[tex]\[ f(0) = 6 \][/tex]
