Which statement holds true for absolute value functions?

Absolute value functions are a fundamental concept in mathematics that represent the distance of a number from zero on the number line. They are written in the form |x|, where x is any real number. When dealing with absolute value functions, it is important to understand the properties that hold true for them.

**Which statement holds true for absolute value functions?**

The statement that holds true for absolute value functions is that the absolute value of any real number is always non-negative. This means that the result of an absolute value function is either zero or a positive number.

FAQs about absolute value functions:

1. What is the definition of an absolute value function?

An absolute value function is a mathematical function that returns the distance of a number from zero on the number line, always resulting in a non-negative value.

2. How is an absolute value function written?

An absolute value function is typically written in the form |x|, where x represents any real number.

3. What are the key properties of absolute value functions?

The key properties of absolute value functions include always returning a non-negative result, being symmetric about the y-axis, and being piecewise defined with different rules for positive and negative input values.

4. How does the graph of an absolute value function look like?

The graph of an absolute value function is V-shaped, with the vertex at the point (0,0) and the arms extending upwards and downwards from the vertex.

5. What happens when the input of an absolute value function is negative?

When the input of an absolute value function is negative, the function will negate the input to make it positive before calculating the absolute value.

6. Can an absolute value function have a negative output?

No, an absolute value function always returns a non-negative output, meaning it can only be zero or a positive number.

7. How is the absolute value of a negative number calculated?

The absolute value of a negative number is equal to the positive equivalent of that number. For example, | -3 | = 3.

8. Are absolute value functions continuous?

Yes, absolute value functions are continuous in their domain, meaning there are no breaks or jumps in the graph.

9. What is the domain and range of an absolute value function?

The domain of an absolute value function is all real numbers, while the range is all non-negative real numbers, including zero.

10. How are absolute value functions used in real-world scenarios?

Absolute value functions are commonly used to represent quantities that cannot be negative, such as distances, magnitudes, or differences between two values.

11. Can absolute value functions be composed with other functions?

Yes, absolute value functions can be composed with other functions to create more complex mathematical expressions and models.

12. Are there any limitations to using absolute value functions?

One limitation of absolute value functions is that they may not be suitable for representing situations where the output can be negative, as the function always returns a non-negative result.

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