 correctly describe the absolute value parent function?

The absolute value parent function is a basic mathematical function that is written as:

\[
f(x) = |x|
\]

### Key characteristics of the absolute value parent function:
1. **Domain**: The domain is all real numbers, \(\mathbb{R}\), because you can input any real number into the function. 
   \[
   \text{Domain: } (-\infty, \infty)
   \]

2. **Range**: The range includes all non-negative real numbers, because the absolute value is always zero or positive. 
   \[
   \text{Range: } [0, \infty)
   \]

3. **Shape**: The graph forms a "V" shape, with the vertex at the origin (0,0). The graph is symmetrical about the y-axis.

4. **Slope**: For \(x \geq 0\), the slope is 1, and for \(x < 0\), the slope is -1.

5. **Intercept**: The function intersects the y-axis at \(y = 0\), because \(|0| = 0\).

### Piecewise representation:
\[
f(x) = 
\begin{cases} 
x & \text{if } x \geq 0 \\
-x & \text{if } x < 0
\end{cases}
\]

This function essentially measures the distance of any number from zero on the number line.

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Would you like more details or have any questions about this? Here are 5 related questions to explore:

1. How do transformations affect the absolute value parent function?
2. What happens when the absolute value function is shifted horizontally or vertically?
3. How do you find the vertex of a transformed absolute value function?
4. What is the real-world significance of the absolute value function?
5. How is the absolute value function related to piecewise functions?

**Tip:** The absolute value function is often used to model situations where only the magnitude matters, such as distance or error.

correctly describe the absolute value parent function?

Explore the absolute value parent function f(x) = |x|, its domain, range, and graphical representation. Learn about its key characteristics, including piecewise representation and slope. Suitable for students in Grades 9-11.

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