Note: These problems are NOT for a grade. ### Transformations of Functions#### a) $ y = \frac{1}{2} f(-x) $- **Domain:** - _Input Box for Domain with Feedback:_ - Incorrect. Tries 3/99 [Previous Tries]- **Range:** - _Input Box for Range with Feedback:_ - Tries 0/99#### b) $ y = -f(3x) $- **Domain:** - _Input Box for Domain with Feedback:_ - Incorrect. Tries 1/99 [Previous Tries]- **Range:** - _Input Box for Range with Feedback:_ - Tries 0/99---This page provides fields for inputting the domain and range of transformed functions and tracks the number of attempts students have made. If a submission is incorrect, feedback is provided, allowing students to revise their answers accordingly. Let $ y = f(x) $ be a function with domain $ D = [0, \infty) $ and range $ R = (-\infty, 0] $. Find the domain $ D $ and range $ R $ for the following functions and enter your answers using interval notation. Be sure your intervals are in the correct order, and enter exact answers only (no approximations).

Name: Note: These problems are NOT for a grade. ### Transformations of Funct
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Description: Note: These problems are NOT for a grade. ### Transformations of Functions#### a) $ y = \frac{1}{2} f(-x) $- **Domain:** - _Input Box for Domain with Feedback:_ - Incorrect. Tries 3/99 [Previous Tries]- **Range:** - _Input Box for Range with F

Consider the domain and range for the function f(x). For fx, D=0,∞R=−∞,0 (a) First, calculate the…

Answered: a) у 3 f(-x) Domain: Submit Answer…

Algebra and Trigonometry (6th Edition)

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ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Note: These problems are NOT for a grade.

### Transformations of Functions

#### a) $ y = \frac{1}{2} f(-x) $

- **Domain:**
- _Input Box for Domain with Feedback:_
- Incorrect. Tries 3/99 [Previous Tries]

- **Range:**
- _Input Box for Range with Feedback:_
- Tries 0/99

#### b) $ y = -f(3x) $

- **Domain:**
- _Input Box for Domain with Feedback:_
- Incorrect. Tries 1/99 [Previous Tries]

- **Range:**
- _Input Box for Range with Feedback:_
- Tries 0/99

---

This page provides fields for inputting the domain and range of transformed functions and tracks the number of attempts students have made. If a submission is incorrect, feedback is provided, allowing students to revise their answers accordingly.

Let $ y = f(x) $ be a function with domain $ D = [0, \infty) $ and range $ R = (-\infty, 0] $. Find the domain $ D $ and range $ R $ for the following functions and enter your answers using interval notation. Be sure your intervals are in the correct order, and enter exact answers only (no approximations).

Expert Solution

Step 1

Consider the domain and range for the function f(x).

$\begin{matrix} F o r f (x), D = [0, \infty) \\ R = (- \infty, 0] \end{matrix}$

(a)

First, calculate the domain and range for the function $y = f (- x)$ from the function $y = f (x)$ .

The function $y = f (- x)$ is obtained from $y = f (x)$ by taking the mirror image about y - axis. So, $y = f (x)$ is defined for positive values for x. After the mirror image about y-axis $y = f (- x)$ is defined for negative values for x.

The range for $y = f (- x)$ remains same as for $y = f (x)$ .

$\begin{array}{rcl} F o r y & = & f (- x), D = (- \infty, 0] \\ R & = & (- \infty, 0] \end{array}$

Now, calculate the domain and range for the function $y = \frac{1}{2} f (- x)$ from the function $y = f (- x)$ .

The range remains same for $y = \frac{1}{2} f (- x)$ and $y = f (- x)$ as a constant 1/2 is multiplied to $y = f (- x)$ .

Also, the range remains the same for $y = \frac{1}{2} f (- x)$ and $y = f (- x)$ as a constant 1/2 is multiplied to $y = f (- x)$ .

$\begin{array}{rcl} H e n c e, f o r y & = & \frac{1}{2} f (- x), \\ D = (- \infty, 0] R = (- \infty, 0] \end{array}$

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