Type The Correct Answer In Each Box. Use Numerals Instead Of Words.Complete The Table Of Inputs And Outputs For The Function.$ F(x) = -5(x + 7) $\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -9 & $\square$ \\ \hline $\square$ &

Type the Correct Answer in Each Box: Completing the Table of Inputs and Outputs for the Function

Understanding the Function

The given function is $f(x) = -5(x + 7)$. This is a linear function, which means it has a constant rate of change. The function is in the form of $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Breaking Down the Function

To understand the function better, let's break it down into its components. The function can be rewritten as $f(x) = -5x - 35$. This shows that the function has a slope of $-5$ and a y-intercept of $-35$.

Completing the Table of Inputs and Outputs

Now, let's complete the table of inputs and outputs for the function.

\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -9 & $\square$ \\ \hline $\square$ & \\ \hline \end{tabular}

To complete the table, we need to find the value of $f(-9)$ and the value of $x$ that corresponds to $f(x) = 0$.

Finding the Value of $f(-9)$

To find the value of $f(-9)$, we substitute $x = -9$ into the function.

$f(-9) = -5(-9 + 7)$ $f(-9) = -5(-2)$ $f(-9) = 10$

So, the value of $f(-9)$ is $10$.

Finding the Value of $x$ that Corresponds to $f(x) = 0$

To find the value of $x$ that corresponds to $f(x) = 0$, we set the function equal to $0$ and solve for $x$.

$-5(x + 7) = 0$ $x + 7 = 0$ $x = -7$

So, the value of $x$ that corresponds to $f(x) = 0$ is $-7$.

Completing the Table

Now that we have found the values of $f(-9)$ and $x$ that corresponds to $f(x) = 0$, we can complete the table.

\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -9 & $10$ \\ \hline $-7$ & $0$ \\ \hline \end{tabular}

Conclusion

In this article, we have completed the table of inputs and outputs for the function $f(x) = -5(x + 7)$. We have found the value of $f(-9)$ and the value of $x$ that corresponds to $f(x) = 0$. The completed table is shown above.

Key Takeaways

• The function $f(x) = -5(x + 7)$ is a linear function with a slope of $-5$ and a y-intercept of $-35$.
• The value of $f(-9)$ is $10$.
• The value of $x$ that corresponds to $f(x) = 0$ is $-7$.

Discussion Category: Mathematics

This article is related to the field of mathematics, specifically to the topic of functions and linear equations. The article provides a step-by-step guide on how to complete the table of inputs and outputs for a given function. The article is suitable for students who are studying mathematics and need to understand how to work with functions and linear equations.
Q&A: Completing the Table of Inputs and Outputs for the Function

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to completing the table of inputs and outputs for the function $f(x) = -5(x + 7)$.

Q: What is the slope of the function $f(x) = -5(x + 7)$?

A: The slope of the function $f(x) = -5(x + 7)$ is $-5$. This means that for every unit increase in $x$, the value of $f(x)$ decreases by $5$ units.

Q: What is the y-intercept of the function $f(x) = -5(x + 7)$?

A: The y-intercept of the function $f(x) = -5(x + 7)$ is $-35$. This means that when $x = 0$, the value of $f(x)$ is $-35$.

Q: How do I find the value of $f(-9)$?

A: To find the value of $f(-9)$, you need to substitute $x = -9$ into the function. This will give you $f(-9) = -5(-9 + 7) = -5(-2) = 10$.

Q: How do I find the value of $x$ that corresponds to $f(x) = 0$?

A: To find the value of $x$ that corresponds to $f(x) = 0$, you need to set the function equal to $0$ and solve for $x$. This will give you $-5(x + 7) = 0$, which simplifies to $x + 7 = 0$. Solving for $x$, you get $x = -7$.

Q: What is the completed table of inputs and outputs for the function $f(x) = -5(x + 7)$?

A: The completed table of inputs and outputs for the function $f(x) = -5(x + 7)$ is shown below.

\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -9 & $10$ \\ \hline $-7$ & $0$ \\ \hline \end{tabular}

Q: What is the significance of the completed table of inputs and outputs?

A: The completed table of inputs and outputs is significant because it shows the relationship between the input values of $x$ and the corresponding output values of $f(x)$. This can be useful for understanding the behavior of the function and making predictions about its values.

Q: How can I use the completed table of inputs and outputs to solve problems?

A: You can use the completed table of inputs and outputs to solve problems by substituting different values of $x$ into the table and finding the corresponding values of $f(x)$. This can be useful for solving equations and inequalities involving the function.

Conclusion

In this article, we have answered some frequently asked questions related to completing the table of inputs and outputs for the function $f(x) = -5(x + 7)$. We have also provided a completed table of inputs and outputs and discussed its significance and applications.

Key Takeaways

• The slope of the function $f(x) = -5(x + 7)$ is $-5$.
• The y-intercept of the function $f(x) = -5(x + 7)$ is $-35$.
• The value of $f(-9)$ is $10$.
• The value of $x$ that corresponds to $f(x) = 0$ is $-7$.
• The completed table of inputs and outputs for the function $f(x) = -5(x + 7)$ is shown above.

Discussion Category: Mathematics

This article is related to the field of mathematics, specifically to the topic of functions and linear equations. The article provides a step-by-step guide on how to complete the table of inputs and outputs for a given function and answers some frequently asked questions related to this topic. The article is suitable for students who are studying mathematics and need to understand how to work with functions and linear equations.