Piecewise Representation of F(x) = |x+4|

Math Problem Statement

F(x) = |x+4| mutlak değer fonksiyonunu parçalı fonksiyon olarak gösteriniz?

The question is asking for the piecewise representation of the absolute value function $F(x) = |x+4|$ .

The absolute value function can be broken into two cases depending on whether the expression inside the absolute value is non-negative or negative.

This simplifies to: $F(x) = x + 4, \quad \text{for } x \geq -4.$

For this case, the absolute value reverses the sign: $F(x) = -(x + 4) = -x - 4, \quad \text{for } x < -4.$

Combining the two cases, the piecewise definition of $F(x)$ is:

\begin{cases} x + 4, & \text{if } x \geq -4, \\ -x - 4, & \text{if } x < -4. \end{cases}$$ Let me know if you'd like additional explanations or visualizations! 😊 --- ### Questions to Expand Your Understanding: 1. How does the graph of $$F(x) = |x+4|$$ look, and how can you plot it? 2. What is the domain and range of $$F(x) = |x+4|$$? 3. How does the point of transition ($$x = -4$$) influence the graph? 4. How does the function $$F(x) = |x+4|$$ differ from $$G(x) = |x|$$? 5. How can absolute value functions be used in real-world applications? --- ### Tip: To analyze any absolute value function, always break it into cases based on the sign of the expression inside the absolute value!

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Absolute Value Functions
Piecewise Functions

|a| = a if a >= 0, |a| = -a if a < 0

Absolute Value Property

Grades 9-10

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