Complete The Table.$\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{$f(x)=-2|x|$} \\ \hline $x$ & $f(x)$ \\ \hline -2 & $\square$ \\ \hline 0 & $\square$ \\ \hline 2 & $\square$ \\ \hline 4 & $\square$

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Understanding and Completing the Table for the Function f(x) = -2|x|

In mathematics, functions are used to describe the relationship between two variables. The function f(x) = -2|x| is a type of absolute value function, which is a function that involves the absolute value of a variable. In this article, we will explore the function f(x) = -2|x| and complete the table for this function.

What is an Absolute Value Function?

An absolute value function is a function that involves the absolute value of a variable. The absolute value of a number is its distance from zero on the number line. For example, the absolute value of -3 is 3, and the absolute value of 4 is 4. Absolute value functions are commonly used in mathematics to model real-world problems that involve distances or magnitudes.

The Function f(x) = -2|x|

The function f(x) = -2|x| is a type of absolute value function. The absolute value of x is denoted by |x|, and the function is multiplied by -2. This means that the function will have a negative value for all values of x, except when x is equal to 0.

Completing the Table

To complete the table for the function f(x) = -2|x|, we need to find the values of f(x) for x = -2, 0, 2, and 4.

x = -2

When x = -2, the absolute value of x is 2. Therefore, f(-2) = -2|x| = -2(2) = -4.

x = 0

When x = 0, the absolute value of x is 0. Therefore, f(0) = -2|x| = -2(0) = 0.

x = 2

When x = 2, the absolute value of x is 2. Therefore, f(2) = -2|x| = -2(2) = -4.

x = 4

When x = 4, the absolute value of x is 4. Therefore, f(4) = -2|x| = -2(4) = -8.

Completed Table

x f(x)
-2 -4
0 0
2 -4
4 -8

Discussion

The function f(x) = -2|x| is a type of absolute value function that has a negative value for all values of x, except when x is equal to 0. The completed table shows that the function has a value of -4 when x = -2 and 2, and a value of -8 when x = 4.

Conclusion

In conclusion, the function f(x) = -2|x| is a type of absolute value function that has a negative value for all values of x, except when x is equal to 0. The completed table shows that the function has a value of -4 when x = -2 and 2, and a value of -8 when x = 4. This function can be used to model real-world problems that involve distances or magnitudes.

References

In our previous article, we explored the function f(x) = -2|x| and completed the table for this function. In this article, we will answer some frequently asked questions (FAQs) about the function f(x) = -2|x|.

Q: What is the domain of the function f(x) = -2|x|?

A: The domain of the function f(x) = -2|x| is all real numbers, denoted by (-∞, ∞). This means that the function is defined for all values of x.

Q: What is the range of the function f(x) = -2|x|?

A: The range of the function f(x) = -2|x| is all non-positive real numbers, denoted by (-∞, 0]. This means that the function will always have a non-positive value.

Q: Is the function f(x) = -2|x| an even function?

A: Yes, the function f(x) = -2|x| is an even function. This means that f(-x) = f(x) for all values of x.

Q: Is the function f(x) = -2|x| a one-to-one function?

A: No, the function f(x) = -2|x| is not a one-to-one function. This means that there are multiple values of x that map to the same value of f(x).

Q: How do I graph the function f(x) = -2|x|?

A: To graph the function f(x) = -2|x|, you can use a graphing calculator or a computer algebra system. You can also graph the function by plotting points on a coordinate plane. The graph of the function will be a V-shaped graph that opens downwards.

Q: Can I use the function f(x) = -2|x| to model real-world problems?

A: Yes, you can use the function f(x) = -2|x| to model real-world problems that involve distances or magnitudes. For example, you can use this function to model the distance between two points on a coordinate plane.

Q: How do I find the inverse of the function f(x) = -2|x|?

A: To find the inverse of the function f(x) = -2|x|, you can use the following steps:

  1. Replace f(x) with y.
  2. Swap x and y.
  3. Solve for y.

The inverse of the function f(x) = -2|x| is f^(-1)(x) = -x/2.

Conclusion

In conclusion, the function f(x) = -2|x| is a type of absolute value function that has a negative value for all values of x, except when x is equal to 0. The completed table shows that the function has a value of -4 when x = -2 and 2, and a value of -8 when x = 4. This function can be used to model real-world problems that involve distances or magnitudes.

References