Not simplifying the answers

Oct 13, 2025 by vinooalluri.com 20 views

Understanding the Function Rule

The given function rule is $f(x)=\sqrt{x}-3$ . This function takes an input value $x$ , finds its square root, and then subtracts 3 from it. To fill in the table, we need to apply this function rule to each input value in the table.

Filling in the Table

We will start by filling in the table with the given input values and their corresponding output values using the function rule.

Input Value 1: $x=0$

To find the output value for $x=0$ , we substitute 0 into the function rule:

$f(0)=\sqrt{0}-3$

Since the square root of 0 is 0, we have:

$f(0)=0-3=-3$

So, the output value for $x=0$ is -3.

Input Value 2: $x=4$

To find the output value for $x=4$ , we substitute 4 into the function rule:

$f(4)=\sqrt{4}-3$

Since the square root of 4 is 2, we have:

$f(4)=2-3=-1$

So, the output value for $x=4$ is -1.

Input Value 3: $x=9$

To find the output value for $x=9$ , we substitute 9 into the function rule:

$f(9)=\sqrt{9}-3$

Since the square root of 9 is 3, we have:

$f(9)=3-3=0$

So, the output value for $x=9$ is 0.

Simplifying the Answers

We have filled in the table with the output values for each input value. However, we need to simplify our answers as much as possible.

Output Value 1: $f(0)=-3$

The output value for $x=0$ is already simplified, so we don't need to do anything.

Output Value 2: $f(4)=-1$

The output value for $x=4$ is already simplified, so we don't need to do anything.

Output Value 3: $f(9)=0$

The output value for $x=9$ is already simplified, so we don't need to do anything.

Conclusion

We have filled in the table using the function rule $f(x)=\sqrt{x}-3$ and simplified our answers as much as possible. The final table is:

$x$	$f(x)$
0	-3
4	-1
9	0

Discussion

The function rule $f(x)=\sqrt{x}-3$ is a simple example of a function that involves the square root of the input value. The table shows how the function rule can be applied to different input values to produce different output values. This type of function is commonly used in mathematics and has many real-world applications.

Real-World Applications

The function rule $f(x)=\sqrt{x}-3$ has many real-world applications, including:

Physics: The function rule can be used to model the motion of an object that is moving at a constant velocity. The input value $x$ represents time, and the output value $f(x)$ represents the position of the object.
Engineering: The function rule can be used to design and optimize systems that involve the square root of a value. For example, in the design of a bridge, the function rule can be used to calculate the stress on the bridge due to the weight of the traffic.
Computer Science: The function rule can be used to develop algorithms that involve the square root of a value. For example, in the development of a search engine, the function rule can be used to calculate the relevance of a web page to a search query.

Conclusion

In conclusion, the function rule $f(x)=\sqrt{x}-3$ is a simple example of a function that involves the square root of the input value. The table shows how the function rule can be applied to different input values to produce different output values. This type of function is commonly used in mathematics and has many real-world applications.

Frequently Asked Questions

We have filled in the table using the function rule $f(x)=\sqrt{x}-3$ and simplified our answers as much as possible. However, we know that there are many more questions that our readers might have. In this article, we will answer some of the most frequently asked questions about the function rule and the table.

Q: What is the function rule $f(x)=\sqrt{x}-3$ ?

A: The function rule $f(x)=\sqrt{x}-3$ is a mathematical function that takes an input value $x$ , finds its square root, and then subtracts 3 from it.

Q: How do I fill in the table using the function rule?

A: To fill in the table, you need to substitute each input value into the function rule and calculate the output value. For example, if the input value is 0, you would substitute 0 into the function rule and calculate the output value as follows:

$f(0)=\sqrt{0}-3$

Since the square root of 0 is 0, the output value is -3.

Q: What if the input value is a negative number?

A: If the input value is a negative number, the square root of the number is not a real number. In this case, you would need to click "Not a real number" in the table.

Q: Can I use the function rule to model real-world phenomena?

A: Yes, the function rule $f(x)=\sqrt{x}-3$ can be used to model real-world phenomena that involve the square root of a value. For example, in physics, the function rule can be used to model the motion of an object that is moving at a constant velocity.

Q: How do I simplify the answers in the table?

A: To simplify the answers in the table, you need to reduce the output values to their simplest form. For example, if the output value is 2-3, you would simplify it to -1.

Q: What are some real-world applications of the function rule?

A: The function rule $f(x)=\sqrt{x}-3$ has many real-world applications, including:

Physics: The function rule can be used to model the motion of an object that is moving at a constant velocity.
Engineering: The function rule can be used to design and optimize systems that involve the square root of a value.
Computer Science: The function rule can be used to develop algorithms that involve the square root of a value.

Q: Can I use the function rule to solve problems in other areas of mathematics?

A: Yes, the function rule $f(x)=\sqrt{x}-3$ can be used to solve problems in other areas of mathematics, including algebra, geometry, and trigonometry.

Q: How do I use the function rule to solve problems in other areas of mathematics?

A: To use the function rule to solve problems in other areas of mathematics, you need to apply the function rule to the problem and then use the output value to solve the problem. For example, if you are solving a problem in algebra, you might need to use the function rule to find the value of a variable.

Q: What are some common mistakes to avoid when using the function rule?

A: Some common mistakes to avoid when using the function rule include:

Not simplifying the answers: Make sure to simplify the output values to their simplest form.
Not using the correct input values: Make sure to use the correct input values in the function rule.
Not checking for negative numbers: Make sure to check if the input value is a negative number, and if so, click "Not a real number" in the table.