Math Problem Statement
-1 if z≤-1 Sketch a graph of f(x) = 2x+1 if-1<x<1 2 if 1
Solution
The graph above represents the piecewise function:
\begin{cases} -1, & \text{if } x \leq -1 \\ 2x + 1, & \text{if } -1 < x < 1 \\ 2, & \text{if } x \geq 1 \end{cases}$$ ### Key points: - For $$x \leq -1$$, the function is a constant horizontal line at $$y = -1$$. - For $$-1 < x < 1$$, the function is a line with a slope of 2. - For $$x \geq 1$$, the function is constant at $$y = 2$$. Do you want more details or have any questions? Here are some related questions: 1. How do we identify discontinuities in a piecewise function? 2. What are the key features of linear functions like $$2x + 1$$? 3. How do we find where a piecewise function is continuous? 4. Can this function be differentiated everywhere? Why or why not? 5. How would the graph change if $$f(x) = 3x - 2$$ for $$-1 < x < 1$$? **Tip:** For piecewise functions, check for continuity and differentiability at the transition points between different segments.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Equations
Graphing Functions
Formulas
f(x) = -1 for x ≤ -1
f(x) = 2x + 1 for -1 < x < 1
f(x) = 2 for x ≥ 1
Theorems
Continuity of Piecewise Functions
Slope-Intercept Form of a Line
Suitable Grade Level
Grades 9-12