The Function $f(x$\] Is Given By The Set Of Ordered Pairs:$\{(1,0),(-10,2),(0,6),(3,17),(-2,-1)\}$Which Equation Is True?A. $f(-10)=1$ B. $f(2)=-10$ C. $f(0)=6$ D. $f(1)=-10$

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Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is often represented as a set of ordered pairs, where each pair consists of an input value and the corresponding output value. In this article, we will explore the function $f(x)$ given by the set of ordered pairs: $\{(1,0),(-10,2),(0,6),(3,17),(-2,-1)\}$. We will examine each ordered pair and determine which equation is true.

Understanding Ordered Pairs

An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value. In the given set of ordered pairs, we have:

• $(1,0)$: This means that when the input value is $1$, the output value is $0$.
• $(-10,2)$: This means that when the input value is $-10$, the output value is $2$.
• $(0,6)$: This means that when the input value is $0$, the output value is $6$.
• $(3,17)$: This means that when the input value is $3$, the output value is $17$.
• $(-2,-1)$: This means that when the input value is $-2$, the output value is $-1$.

Analyzing the Options

Now that we have a clear understanding of the ordered pairs, let's analyze the options:

A. $f(-10)=1$ B. $f(2)=-10$ C. $f(0)=6$ D. $f(1)=-10$

We can see that option A is not true because the ordered pair $(-10,2)$ indicates that when the input value is $-10$, the output value is $2$, not $1$.

Option B: $f(2)=-10$

We can see that the input value $2$ is not present in any of the ordered pairs. Therefore, we cannot determine the output value for $f(2)$ based on the given set of ordered pairs.

Option C: $f(0)=6$

We can see that the ordered pair $(0,6)$ indicates that when the input value is $0$, the output value is $6$. Therefore, option C is true.

Option D: $f(1)=-10$

We can see that the ordered pair $(1,0)$ indicates that when the input value is $1$, the output value is $0$, not $-10$. Therefore, option D is not true.

Conclusion

In conclusion, the equation that is true is $f(0)=6$. This is because the ordered pair $(0,6)$ indicates that when the input value is $0$, the output value is $6$. We cannot determine the output value for $f(-10)$, $f(2)$, or $f(1)$ based on the given set of ordered pairs.

Key Takeaways

• A function is a relation between a set of inputs and a set of possible outputs.
• An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value.
• We can determine the output value for a given input value by examining the ordered pairs.
• If the input value is not present in any of the ordered pairs, we cannot determine the output value.

Further Reading

If you would like to learn more about functions and ordered pairs, I recommend checking out the following resources:

• Khan Academy: Functions and Relations
• Math Open Reference: Functions
• Wolfram MathWorld: Ordered Pairs

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Q: What is a function?

A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is often represented as a set of ordered pairs, where each pair consists of an input value and the corresponding output value.

Q: What is an ordered pair?

A: An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value.

Q: How do I determine the output value for a given input value?

A: To determine the output value for a given input value, you need to examine the ordered pairs. If the input value is present in one of the ordered pairs, you can find the corresponding output value. If the input value is not present in any of the ordered pairs, you cannot determine the output value.

Q: What if the input value is not present in any of the ordered pairs?

A: If the input value is not present in any of the ordered pairs, you cannot determine the output value. This is because the function is not defined for that particular input value.

Q: Can I have multiple output values for a single input value?

A: No, you cannot have multiple output values for a single input value. This would mean that the function is not well-defined, and it would not be a valid function.

Q: How do I represent a function as a set of ordered pairs?

A: To represent a function as a set of ordered pairs, you need to list each input value and its corresponding output value. For example, if the function is $f(x) = 2x + 1$, you can represent it as the set of ordered pairs: $\{(1,3), (2,5), (3,7)\}$.

Q: Can I have a function with no input values?

A: No, you cannot have a function with no input values. A function must have at least one input value, and it must have a corresponding output value.

Q: Can I have a function with multiple output values for a single input value?

A: No, you cannot have a function with multiple output values for a single input value. This would mean that the function is not well-defined, and it would not be a valid function.

Q: How do I determine if a function is one-to-one or many-to-one?

A: To determine if a function is one-to-one or many-to-one, you need to examine the ordered pairs. If each input value corresponds to a unique output value, the function is one-to-one. If multiple input values correspond to the same output value, the function is many-to-one.

Q: Can I have a function that is both one-to-one and many-to-one?

A: No, you cannot have a function that is both one-to-one and many-to-one. A function can be either one-to-one or many-to-one, but not both.

Q: How do I determine if a function is onto or not?

A: To determine if a function is onto or not, you need to examine the ordered pairs. If every possible output value is present in the ordered pairs, the function is onto. If not, the function is not onto.

Q: Can I have a function that is both one-to-one and onto?

A: Yes, you can have a function that is both one-to-one and onto. This is known as a bijective function.

Q: What is a bijective function?

A: A bijective function is a function that is both one-to-one and onto. It is a function that maps each input value to a unique output value, and every possible output value is present in the ordered pairs.

Q: Can I have a function that is not bijective?

A: Yes, you can have a function that is not bijective. This can happen if the function is not one-to-one or not onto.

Q: How do I determine if a function is bijective?

A: To determine if a function is bijective, you need to examine the ordered pairs. If the function is both one-to-one and onto, it is bijective. If not, it is not bijective.

Q: Can I have a function that is bijective and also has multiple output values for a single input value?

A: No, you cannot have a function that is bijective and also has multiple output values for a single input value. This would mean that the function is not well-defined, and it would not be a valid function.

Q: How do I represent a bijective function as a set of ordered pairs?

A: To represent a bijective function as a set of ordered pairs, you need to list each input value and its corresponding output value. For example, if the function is $f(x) = 2x + 1$, you can represent it as the set of ordered pairs: $\{(1,3), (2,5), (3,7)\}$.