Fill in the blank with the appropriate direction (left, right, up, or down). (a) The graph of y = f(x) – 4 is obtained from the graph of y = f(x) by shifting -Select--- v4 units. %3D (b) The graph of y = f(x - 4) is obtained from the graph of y = f(x) by shifting Select--- 4 units.
Fill in the blank with the appropriate direction (left, right, up, or down). (a) The graph of y = f(x) – 4 is obtained from the graph of y = f(x) by shifting -Select--- v4 units. %3D (b) The graph of y = f(x - 4) is obtained from the graph of y = f(x) by shifting Select--- 4 units.
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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![## DETAILS
### Transformation of Graphs
Fill in the blank with the appropriate direction (left, right, up, or down):
#### (a) The graph of \( y = f(x) - 4 \) is obtained from the graph of \( y = f(x) \) by shifting **[Select]** 4 units.
#### (b) The graph of \( y = f(x - 4) \) is obtained from the graph of \( y = f(x) \) by shifting **[Select]** 4 units.
To understand these transformations:
1. **Vertical Shifts**:
- The equation \( y = f(x) - c \) shifts the graph of \( y = f(x) \) **down** by \( c \) units if \( c \) is positive.
- The equation \( y = f(x) + c \) shifts the graph of \( y = f(x) \) **up** by \( c \) units if \( c \) is positive.
2. **Horizontal Shifts**:
- The equation \( y = f(x - c) \) shifts the graph of \( y = f(x) \) **right** by \( c \) units if \( c \) is positive.
- The equation \( y = f(x + c) \) shifts the graph of \( y = f(x) \) **left** by \( c \) units if \( c \) is positive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f4719ec-89c6-49f2-a8fd-c905fe776b01%2Fefcda949-d0ff-495a-a2f7-10765da03c3b%2Fcw8podr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## DETAILS
### Transformation of Graphs
Fill in the blank with the appropriate direction (left, right, up, or down):
#### (a) The graph of \( y = f(x) - 4 \) is obtained from the graph of \( y = f(x) \) by shifting **[Select]** 4 units.
#### (b) The graph of \( y = f(x - 4) \) is obtained from the graph of \( y = f(x) \) by shifting **[Select]** 4 units.
To understand these transformations:
1. **Vertical Shifts**:
- The equation \( y = f(x) - c \) shifts the graph of \( y = f(x) \) **down** by \( c \) units if \( c \) is positive.
- The equation \( y = f(x) + c \) shifts the graph of \( y = f(x) \) **up** by \( c \) units if \( c \) is positive.
2. **Horizontal Shifts**:
- The equation \( y = f(x - c) \) shifts the graph of \( y = f(x) \) **right** by \( c \) units if \( c \) is positive.
- The equation \( y = f(x + c) \) shifts the graph of \( y = f(x) \) **left** by \( c \) units if \( c \) is positive.
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