19. Graph the following piece wise function. S 1₁ x - 4 x² +3 7 X/Y -5 -}-5½ ₂2 -5-64 f(x) = 14 x < -2 -2 < x < 1 x > 1 20. Using # 19, evaluate: (a) f(-5) (b) f(0) (c) f(6) 19. 10 想服務專版 20. a.). b.) c.) 44
19. Graph the following piece wise function. S 1₁ x - 4 x² +3 7 X/Y -5 -}-5½ ₂2 -5-64 f(x) = 14 x < -2 -2 < x < 1 x > 1 20. Using # 19, evaluate: (a) f(-5) (b) f(0) (c) f(6) 19. 10 想服務專版 20. a.). b.) c.) 44
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do I evaluate using question 19?
![## Educational Content: Piecewise Functions
### Problem 19: Graph the Following Piecewise Function
Given the piecewise function \( f(x) \):
- \[
f(x) =
\begin{cases}
\frac{1}{x^2} - 4 & \text{for } x \leq -2 \\
x^2 + 3 & \text{for } -2 < x \leq 1 \\
7 & \text{for } x > 1
\end{cases}
\]
**Table of Values for \( x \leq -2 \):**
- \( x = -2 \), \( y = -5 \)
- \( x = -3 \), \( y = -5 \frac{1}{2} \)
- \( x = -4 \), \( y = -6 \)
- \( x = -5 \), \( y = -6 \frac{1}{5} \)
**Table of Values for \(-2 < x \leq 1 \):**
- \( x = -1 \), \( y = 4 \)
- \( x = 0 \), \( y = 3 \)
### Graph Description
The graph consists of different sections:
- **For \( x \leq -2 \):** The graph is decreasing as it follows the curve of \( \frac{1}{x^2} - 4 \), indicated by plotted points and a downward trend on the left side of the graph.
- **For \(-2 < x \leq 1 \):** The section is a parabolic curve stemming from the quadratic function \( x^2 + 3 \), showing an upward trend with endpoints marked at the calculated points.
- **For \( x > 1 \):** A horizontal line at \( y = 7 \) indicates the constant nature of this part of the piecewise function.
### Problem 20: Evaluating the Function
Using the results from problem 19, evaluate \( f(x) \) for given values:
#### Evaluation
20.
- a.) \( f(-5) \) = _______
- b.) \( f(0) \) = _______
- c.) \( f(6) \) = _______
The evaluations require utilizing the specific section of the piecewise function applicable to each \( x \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3456819-528d-42b3-b255-e8873e975f3d%2F22829298-2aa5-4131-807d-fadf3b28d0ae%2F1j5bbw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Educational Content: Piecewise Functions
### Problem 19: Graph the Following Piecewise Function
Given the piecewise function \( f(x) \):
- \[
f(x) =
\begin{cases}
\frac{1}{x^2} - 4 & \text{for } x \leq -2 \\
x^2 + 3 & \text{for } -2 < x \leq 1 \\
7 & \text{for } x > 1
\end{cases}
\]
**Table of Values for \( x \leq -2 \):**
- \( x = -2 \), \( y = -5 \)
- \( x = -3 \), \( y = -5 \frac{1}{2} \)
- \( x = -4 \), \( y = -6 \)
- \( x = -5 \), \( y = -6 \frac{1}{5} \)
**Table of Values for \(-2 < x \leq 1 \):**
- \( x = -1 \), \( y = 4 \)
- \( x = 0 \), \( y = 3 \)
### Graph Description
The graph consists of different sections:
- **For \( x \leq -2 \):** The graph is decreasing as it follows the curve of \( \frac{1}{x^2} - 4 \), indicated by plotted points and a downward trend on the left side of the graph.
- **For \(-2 < x \leq 1 \):** The section is a parabolic curve stemming from the quadratic function \( x^2 + 3 \), showing an upward trend with endpoints marked at the calculated points.
- **For \( x > 1 \):** A horizontal line at \( y = 7 \) indicates the constant nature of this part of the piecewise function.
### Problem 20: Evaluating the Function
Using the results from problem 19, evaluate \( f(x) \) for given values:
#### Evaluation
20.
- a.) \( f(-5) \) = _______
- b.) \( f(0) \) = _______
- c.) \( f(6) \) = _______
The evaluations require utilizing the specific section of the piecewise function applicable to each \( x \
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