The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. %3D where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) = – f(x) The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 4 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -3 -4 -5 -6+ 3.
The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. %3D where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) = – f(x) The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 4 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -3 -4 -5 -6+ 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Transformation of Functions**
The transformation of a function \( f(x) \) into a function \( g(x) \) is given by:
\[ g(x) = Af(Bx + H) + K \]
**Where the constants:**
- \( A \) vertically scales the function. (Negative \( A \) reflects the function about the x-axis.)
- \( B \) horizontally scales the function. (Negative \( B \) reflects the function about the y-axis.)
- \( H \) horizontally shifts the function.
- \( K \) vertically shifts the function.
**Exercise:**
Transform \( f(x) \) into \( g(x) \) where the transformation is \( g(x) = -f(x) \).
The function \( f(x) \) is shown below in red. Graph the transformed function \( g(x) \) by first placing a dot at each endpoint of the new transformed function and then click on the "line segment" button to connect the two blue dots.
*Hint: Use pattern-matching to determine the values of the constants \( A, B, H, \) and \( K \).*
**Graph Explanation:**
The red line segment is displayed on a coordinate grid. It starts at the point (-2, 1) and ends at the point (1, -2). The task involves transforming this red segment according to the provided transformation rules. Use the interactive features (Dot and Line Segment) to plot the transformed points and connect them.
**Controls:**
- **Clear All:** Clears the graph.
- **Draw:** Allows selecting between placing a **Dot** or drawing a **Line Segment**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cde6e04-3e17-4552-9462-01a5786ab697%2F2ce979c6-596c-42cd-af22-aff62ccded3a%2F2m9c1vi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transformation of Functions**
The transformation of a function \( f(x) \) into a function \( g(x) \) is given by:
\[ g(x) = Af(Bx + H) + K \]
**Where the constants:**
- \( A \) vertically scales the function. (Negative \( A \) reflects the function about the x-axis.)
- \( B \) horizontally scales the function. (Negative \( B \) reflects the function about the y-axis.)
- \( H \) horizontally shifts the function.
- \( K \) vertically shifts the function.
**Exercise:**
Transform \( f(x) \) into \( g(x) \) where the transformation is \( g(x) = -f(x) \).
The function \( f(x) \) is shown below in red. Graph the transformed function \( g(x) \) by first placing a dot at each endpoint of the new transformed function and then click on the "line segment" button to connect the two blue dots.
*Hint: Use pattern-matching to determine the values of the constants \( A, B, H, \) and \( K \).*
**Graph Explanation:**
The red line segment is displayed on a coordinate grid. It starts at the point (-2, 1) and ends at the point (1, -2). The task involves transforming this red segment according to the provided transformation rules. Use the interactive features (Dot and Line Segment) to plot the transformed points and connect them.
**Controls:**
- **Clear All:** Clears the graph.
- **Draw:** Allows selecting between placing a **Dot** or drawing a **Line Segment**.
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