Answer :
To determine which equation is true, let's evaluate each of the statements using the values given by the set of ordered pairs for the function \( f(x) \):
[tex]\[ \{(1,0),(-10,2),(0,6),(3,17),(-2,-1)\} \][/tex]
### Evaluating Each Statement:
1. Statement: \( f(-10) = 1 \)
We need to check the value of \( f(x) \) when \( x = -10 \).
From the set of ordered pairs, \( f(-10) = 2 \), not 1.
Hence, \( f(-10) = 1 \) is false.
2. Statement: \( f(2) = -10 \)
We need to check if there's a value for \( f(x) \) when \( x = 2 \).
The set of ordered pairs does not contain any pair with \( x = 2 \).
Hence, \( f(2) = -10 \) is not defined, so it's false.
3. Statement: \( f(0) = 6 \)
We need to check the value of \( f(x) \) when \( x = 0 \).
From the set of ordered pairs, \( f(0) = 6 \).
Hence, \( f(0) = 6 \) is true.
4. Statement: \( f(1) = -10 \)
We need to check the value of \( f(x) \) when \( x = 1 \).
From the set of ordered pairs, \( f(1) = 0 \), not -10.
Hence, \( f(1) = -10 \) is false.
### Conclusion:
Among the given statements, the only true statement is:
[tex]\[ f(0) = 6 \][/tex]
[tex]\[ \{(1,0),(-10,2),(0,6),(3,17),(-2,-1)\} \][/tex]
### Evaluating Each Statement:
1. Statement: \( f(-10) = 1 \)
We need to check the value of \( f(x) \) when \( x = -10 \).
From the set of ordered pairs, \( f(-10) = 2 \), not 1.
Hence, \( f(-10) = 1 \) is false.
2. Statement: \( f(2) = -10 \)
We need to check if there's a value for \( f(x) \) when \( x = 2 \).
The set of ordered pairs does not contain any pair with \( x = 2 \).
Hence, \( f(2) = -10 \) is not defined, so it's false.
3. Statement: \( f(0) = 6 \)
We need to check the value of \( f(x) \) when \( x = 0 \).
From the set of ordered pairs, \( f(0) = 6 \).
Hence, \( f(0) = 6 \) is true.
4. Statement: \( f(1) = -10 \)
We need to check the value of \( f(x) \) when \( x = 1 \).
From the set of ordered pairs, \( f(1) = 0 \), not -10.
Hence, \( f(1) = -10 \) is false.
### Conclusion:
Among the given statements, the only true statement is:
[tex]\[ f(0) = 6 \][/tex]
