2. Function below is tanslated 3 units right, Then reflected across the y-ands to create function. Which equation represents g? A. g(x)=√(x-1) B. g(x)=√x+1) C. g(x)=-1 D. e(x)--+1
2. Function below is tanslated 3 units right, Then reflected across the y-ands to create function. Which equation represents g? A. g(x)=√(x-1) B. g(x)=√x+1) C. g(x)=-1 D. e(x)--+1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:The image contains a mathematical question about transformations of a function and provides multiple-choice options. The question and details are as follows:
### Question
2. Function \( f \) (below) is translated 3 units right, then reflected across the y-axis to create function \( g \). Which equation represents \( g \)?
### Graph Description
The graph of function \( f(x) = \sqrt{x} \) is shown on a coordinate grid. The function is a square root function starting at the origin (0,0) and increasing gradually to the right.
### Answer Choices
- **A.** \( g(x) = \sqrt{-(x-3)} \)
- **B.** \( g(x) = \sqrt{x+3} \)
- **C.** \( g(x) = -\sqrt{x-1} \)
- **D.** \( g(x) = -\sqrt{x} + 1 \)
### Answer Selection
- ( ) A
- ( ) B
- ( ) C
- ( ) D
- ( ) E: All of the Above
This question involves understanding the transformation of the square root function: translating it to the right and reflecting across the y-axis. Note that choice E is an option, indicating all of the above might be considered correct depending on interpretation, but usually one specific transformation meets the condition precisely.
Expert Solution
Step 1: Concept of Graph
To translate a function 3 units to the right, you replace x with (x - 3) in the original function.
After that, to reflect it across the y-axis, you replace x with -x.
So, if the original function is f(x), the equation for the reflected and translated function g(x) would be:
So, g(x) is the result of first translating f(x) 3 units to the right and then reflecting it across the y-axis.
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