Math Problem Statement

The image shows a piecewise function f(x) defined as: f(x) = { 2x + 1, for x < 0 and 2x + 2, for x ≥ 0 }

Solution

The image shows a piecewise function f(x)f(x) defined as:

2x + 1, & \text{if } x < 0 \\ 2x + 2, & \text{if } x \geq 0 \end{cases}$$ This means that the function takes different expressions depending on whether $$x$$ is less than 0 or greater than or equal to 0. - When $$x < 0$$, the function is $$f(x) = 2x + 1$$. - When $$x \geq 0$$, the function is $$f(x) = 2x + 2$$. Would you like more details on how to analyze or graph this piecewise function? Here are 5 related questions you can explore: 1. How do you graph a piecewise function? 2. What are the domain and range of this function? 3. Is this piecewise function continuous? Why or why not? 4. How do you evaluate this function for a specific value of $$x$$? 5. How can we find the derivative of this piecewise function? **Tip**: When graphing piecewise functions, plot each piece on its respective interval and ensure you indicate whether endpoints are included or excluded using open or closed circles.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Linear Functions

Formulas

f(x) = 2x + 1 for x < 0
f(x) = 2x + 2 for x ≥ 0

Theorems

Continuity in Piecewise Functions

Suitable Grade Level

Grades 9-12