Complete The Table For The Function $f(x) = |x + 1|$.$\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{$f(x) = |x + 1|$} \\ \hline $x$ & $f(x)$ \\ \hline -10 & $\square$ \\ \hline -5 & $\square$ \\ \hline 0 & $\square$ \\ \hline 5 &

Introduction

In this article, we will be completing the table for the function $f(x) = |x + 1|$. This function is a simple absolute value function, which is a fundamental concept in mathematics. The absolute value function is defined as the distance of a number from zero on the number line. In this case, the function $f(x) = |x + 1|$ represents the distance of a number $x$ from $-1$ on the number line.

Understanding the Absolute Value Function

The absolute value function is a mathematical function that returns the distance of a number from zero on the number line. It is denoted by the symbol $|x|$ and is defined as:

$$|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}$$

In the case of the function $f(x) = |x + 1|$, we need to consider two cases:

• If $x + 1 \geq 0$, then $f(x) = x + 1$
• If $x + 1 < 0$, then $f(x) = -(x + 1)$

Completing the Table

Now that we have understood the absolute value function, let's complete the table for the function $f(x) = |x + 1|$.

Completed Table

Here is the completed table for the function $f(x) = |x + 1|$:

Conclusion

In this article, we have completed the table for the function $f(x) = |x + 1|$. We have understood the absolute value function and evaluated the function for each value of $x$. The completed table shows the values of the function for different inputs.

References

• Absolute Value Function
• Mathematics

Discussion Category: Mathematics

Introduction

In our previous article, we completed the table for the function $f(x) = |x + 1|$. In this article, we will answer some frequently asked questions related to the function and its table.

Q: What is the absolute value function?

A: The absolute value function is a mathematical function that returns the distance of a number from zero on the number line. It is denoted by the symbol $|x|$ and is defined as:

$$|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}$$

Q: How do I evaluate the function $f(x) = |x + 1|$?

A: To evaluate the function $f(x) = |x + 1|$, you need to consider two cases:

• If $x + 1 \geq 0$, then $f(x) = x + 1$
• If $x + 1 < 0$, then $f(x) = -(x + 1)$

Q: What is the value of $f(-10)$?

A: To find the value of $f(-10)$, we need to evaluate the function $f(x) = |x + 1|$ at $x = -10$. Since $-10 + 1 = -9 < 0$, we have $f(-10) = -(-10 + 1) = -(-9) = 9$

Q: What is the value of $f(5)$?

A: To find the value of $f(5)$, we need to evaluate the function $f(x) = |x + 1|$ at $x = 5$. Since $5 + 1 = 6 \geq 0$, we have $f(5) = 5 + 1 = 6$

Q: How do I complete the table for the function $f(x) = |x + 1|$?

A: To complete the table for the function $f(x) = |x + 1|$, you need to evaluate the function at each value of $x$ in the table. For each value of $x$, you need to consider two cases:

• If $x + 1 \geq 0$, then $f(x) = x + 1$
• If $x + 1 < 0$, then $f(x) = -(x + 1)$

Q: What is the completed table for the function $f(x) = |x + 1|$?

A: Here is the completed table for the function $f(x) = |x + 1|$:

Conclusion

In this article, we have answered some frequently asked questions related to the function $f(x) = |x + 1|$ and its table. We have provided a detailed explanation of the absolute value function and evaluated the function for different inputs. The completed table is provided at the end of the article.

References

• Absolute Value Function
• Mathematics

Discussion Category: Mathematics

This article is part of the discussion category: mathematics. The topic of the article is the completion of the table for the function $f(x) = |x + 1|$. The article provides a detailed explanation of the absolute value function and evaluates the function for different inputs. The completed table is provided at the end of the article.