Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Graph the equation and tell if it’s continuous
![**Title:** Graphing a Piecewise-Defined Function
**Description:**
**Function Definition:**
Suppose that the function \( f \) is defined for all real numbers as follows:
\[
f(x) = \begin{cases}
-10 + x^2 & \text{if } -4 \leq x < 4 \\
x + 10 & \text{if } x \geq 4
\end{cases}
\]
**Instructions:**
Graph the function \( f \). Then determine whether or not the function is continuous across its domain.
**Graph Description:**
The graph below should accurately represent the piecewise function defined above. The x-axis ranges from approximately -12 to 12, and the y-axis ranges from about -2 to 12. The graph should depict two distinct segments:
1. **Segment 1:** A parabola opening upwards with the vertex likely below the x-axis, defined by \( -10 + x^2 \) over the interval \(-4 \leq x < 4\).
2. **Segment 2:** A straight line with a positive slope, defined by \( x + 10 \) beginning at \( x = 4 \) and extending towards positive x-values.
Ensure to correctly plot and distinguish these segments with proper domain restrictions. Use open or closed circles as needed to indicate whether endpoints are included in each segment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b2e36ef-961b-444d-a864-96fbb40c42e3%2F0970820e-8c11-45f0-a58d-78da7539b371%2Fs3kwkap_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Graphing a Piecewise-Defined Function
**Description:**
**Function Definition:**
Suppose that the function \( f \) is defined for all real numbers as follows:
\[
f(x) = \begin{cases}
-10 + x^2 & \text{if } -4 \leq x < 4 \\
x + 10 & \text{if } x \geq 4
\end{cases}
\]
**Instructions:**
Graph the function \( f \). Then determine whether or not the function is continuous across its domain.
**Graph Description:**
The graph below should accurately represent the piecewise function defined above. The x-axis ranges from approximately -12 to 12, and the y-axis ranges from about -2 to 12. The graph should depict two distinct segments:
1. **Segment 1:** A parabola opening upwards with the vertex likely below the x-axis, defined by \( -10 + x^2 \) over the interval \(-4 \leq x < 4\).
2. **Segment 2:** A straight line with a positive slope, defined by \( x + 10 \) beginning at \( x = 4 \) and extending towards positive x-values.
Ensure to correctly plot and distinguish these segments with proper domain restrictions. Use open or closed circles as needed to indicate whether endpoints are included in each segment.
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