Answer :
Let's solve this step by step by evaluating which given equation is true based on the function [tex]\( f(x) \)[/tex] defined by the set of ordered pairs. The function is represented by:
[tex]\[ f(x) = \{(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)\} \][/tex]
We need to evaluate the following equations one by one:
1. [tex]\( f(-10) = 1 \)[/tex]
2. [tex]\( f(2) = -10 \)[/tex]
3. [tex]\( f(0) = 6 \)[/tex]
4. [tex]\( f(1) = -10 \)[/tex]
### Evaluating [tex]\( f(-10) = 1 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(-10) \)[/tex]:
[tex]\[ f(-10) = 2 \][/tex]
So, the equation [tex]\( f(-10) = 1 \)[/tex]:
[tex]\[ 2 = 1 \][/tex]
This is false.
### Evaluating [tex]\( f(2) = -10 \)[/tex]
We need to find the value of [tex]\( f(2) \)[/tex]. However, looking at the set of ordered pairs, 2 is not a value of [tex]\( x \)[/tex] provided in our function definition. Therefore:
[tex]\[ f(2) \text{ is undefined} \][/tex]
Thus, the equation [tex]\( f(2) = -10 \)[/tex] is false.
### Evaluating [tex]\( f(0) = 6 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = 6 \][/tex]
So, the equation [tex]\( f(0) = 6 \)[/tex]:
[tex]\[ 6 = 6 \][/tex]
This is true.
### Evaluating [tex]\( f(1) = -10 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = 0 \][/tex]
So, the equation [tex]\( f(1) = -10 \)[/tex]:
[tex]\[ 0 = -10 \][/tex]
This is false.
### Conclusion
After evaluating all the given equations, the only true equation is:
[tex]\[ f(0) = 6 \][/tex]
[tex]\[ f(x) = \{(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)\} \][/tex]
We need to evaluate the following equations one by one:
1. [tex]\( f(-10) = 1 \)[/tex]
2. [tex]\( f(2) = -10 \)[/tex]
3. [tex]\( f(0) = 6 \)[/tex]
4. [tex]\( f(1) = -10 \)[/tex]
### Evaluating [tex]\( f(-10) = 1 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(-10) \)[/tex]:
[tex]\[ f(-10) = 2 \][/tex]
So, the equation [tex]\( f(-10) = 1 \)[/tex]:
[tex]\[ 2 = 1 \][/tex]
This is false.
### Evaluating [tex]\( f(2) = -10 \)[/tex]
We need to find the value of [tex]\( f(2) \)[/tex]. However, looking at the set of ordered pairs, 2 is not a value of [tex]\( x \)[/tex] provided in our function definition. Therefore:
[tex]\[ f(2) \text{ is undefined} \][/tex]
Thus, the equation [tex]\( f(2) = -10 \)[/tex] is false.
### Evaluating [tex]\( f(0) = 6 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = 6 \][/tex]
So, the equation [tex]\( f(0) = 6 \)[/tex]:
[tex]\[ 6 = 6 \][/tex]
This is true.
### Evaluating [tex]\( f(1) = -10 \)[/tex]
According to the set of ordered pairs, we find the value of [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = 0 \][/tex]
So, the equation [tex]\( f(1) = -10 \)[/tex]:
[tex]\[ 0 = -10 \][/tex]
This is false.
### Conclusion
After evaluating all the given equations, the only true equation is:
[tex]\[ f(0) = 6 \][/tex]
