Math Problem Statement
The function f(x) = |x| written as a piecewise function looks like: f(x) = { x if x >= 0, -x if x < 0 }. Please select the best answer from the choices provided (T/F).
Solution
The image asks if the function written as a piecewise function is correctly represented as:
\begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$ This is the correct representation of the absolute value function, $$|x|$$, in piecewise form. For non-negative $$x$$, the value of $$f(x)$$ is $$x$$, and for negative $$x$$, the value of $$f(x)$$ is $$-x$$. Thus, the correct answer is **T** (True). Would you like further clarification on this? Here are five related questions you might explore: 1. How do you graph the function $$f(x) = |x|$$? 2. How can piecewise functions be used in real-life applications? 3. What is the derivative of $$f(x) = |x|$$ and where is it undefined? 4. How does the piecewise form help in understanding the behavior of functions like $$|x|$$? 5. How does the absolute value function relate to distance on the number line? **Tip**: When working with piecewise functions, always check the conditions carefully to ensure you're applying the correct formula based on the value of $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Piecewise Functions
Absolute Value
Formulas
f(x) = |x| = { x if x >= 0, -x if x < 0 }
Theorems
Absolute Value Function
Suitable Grade Level
Grades 6-9