### Given Functions and Transformations#### OverviewThe provided mathematical functions and transformation are as follows:- Given $ f(x) = |x| $- Another function $ g(x) = \frac{1}{2}f(x) - 4.5 $#### Description of TransformationThe transformation from $ f(x) $ to $ g(x) $ involves the following steps:1. **Vertical Compression**: The function $ f(x) $, which is the absolute value function $ |x| $, is vertically compressed by a factor of $ \frac{1}{2} $. This means that for every output value of $ f(x) $, the corresponding value of $ g(x) $ will be half as large.2. **Vertical Translation**: After the initial compression, the resulting function is then shifted downwards by 4.5 units. This translates every point on the function $ \frac{1}{2} |x| $ downward along the y-axis by 4.5 units.By understanding these transformations, learners can visualize and analyze how the original absolute value function $ f(x) $ is altered to produce $ g(x) $.

Please go through the attached solution.Thankyou . Best regards.

Answered: 1 Given f(x) = |x| & g (x) = 5f (æ) 2…

Math

Algebra

1 Given f(x) = |x| & g (x) = 5f (æ) 2 Describe the transformation from f(x) to g(x)

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,...

See similar textbooks

Related questions

Q: 2) In words, communicate all transformations made on the parent function f(x)=3* to sketch the…

A: The given function is .The aim is to find all the transformations required to sketch the graph of…

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1. Now refer to step two to…

Q: Use the given graph of y = f(x) to graph the function g : g(x) = f(x + 1) + 1

Q: If f(x) and g(x) are two functions defined by f(x) = √(x + 1) g(x) = | x - 1 |, then what is the…

A: To find f(g(9))

Q: Use the graph of y = f(x) to graph the given function g: g(x) = -f(x)

Q: represents

A: False

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

Q: Consider the function P(x) = (x – 3)²(x – 9) - The y-intercept is the point The x-intercept(s)…

A: Please refer to the image below

Q: If f(x) = x + 8 and g(x) = x - 8, (a) f(g(x)) %3D (b) g(f(x)): %3D (c) Thus g(x) is called an…

A: Given, fx=x+8 gx=x-8

Q: If f(x) = x + 3 and g(x) = - 3, (a) f(g(x)) %3D (b) g(f(x)) = %3D (c) Thus g(x) is called an…

A: f(x)=x+3,g(x)=x-3

Q: Let g(x) = VT + 3.

A: Given, g(x)=x2+3

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

Q: 1 x-2 f(x)=- y g(x)=√x

A: To find the composite function

Q: find (f+g)(x) (f-g)(x) (f•g)(x) (f/g)(x) and their domains

Q: Determine a function f such that h(x) = f(g(x)), where g(x) = x + 6, and h(x) = (x+6)¹.

A: given h(x)=f(g(x))f(x)=(x+6)4 g(x)=x+6

Q: h(x) = 1 (x-2)3

A: (a) consider functions f(x) = 1/x3 and g(x) = x - 2. Then, f(g(x)) = f(x - 2)…

Q: 11) Given f(x) = x³ and g(x) = -3(2x)³ + 5, describe the transformations in order from f(x) to g(x)…

A: We can solve the given problem using graphical shifting.

Q: describe in words, the transformation based on f(x). 1. g(x)=3f(x) 2. g(x)=f(1/2x) 3. g(x)=f(x-4)

A: In the given question we have to describe the transformation of function.

Q: If f(x) = z + 5 and g(z) = z - 5, (a) f(9(x)) (b) 9(f(x)) (c) Thus g(z) is called an function of…

A: Given f(x)=x+5 and g(x)=x-5. a. f(g(x)) As g(x)=x-5 we will substitute the value in place of g(x)…

Q: Use the graph of y = f(x) to graph the given function g : g(x) = f(x) - 1

A: Given:y=fxgx=fx-1

Q: If f(x) = x + 7 and g(æ) = x - 7, %3D %3D (a) f(g(x)) %3D (b) g(f(x)) = (c) Thus g(x) is called an…

Question

### Given Functions and Transformations

#### Overview
The provided mathematical functions and transformation are as follows:

- Given $ f(x) = |x| $
- Another function $ g(x) = \frac{1}{2}f(x) - 4.5 $

#### Description of Transformation
The transformation from $ f(x) $ to $ g(x) $ involves the following steps:

1. **Vertical Compression**: The function $ f(x) $, which is the absolute value function $ |x| $, is vertically compressed by a factor of $ \frac{1}{2} $. This means that for every output value of $ f(x) $, the corresponding value of $ g(x) $ will be half as large.

2. **Vertical Translation**: After the initial compression, the resulting function is then shifted downwards by 4.5 units. This translates every point on the function $ \frac{1}{2} |x| $ downward along the y-axis by 4.5 units.

By understanding these transformations, learners can visualize and analyze how the original absolute value function $ f(x) $ is altered to produce $ g(x) $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Let f and g be define f(x) = x-5 and g(x)=x²-1. Express the following functions as the sum, difference, quotient, or product or f and g. (a) P(x)=x²-x-4 (b) Q(x)=x² + 2x -9 (c) R(x) = (d) S(x)= = (e) T(x)= x-5 2x²-2 x²-x+4 x-5 x3-4x²-11x+30 v2_1 Given the following, find f(x). (a) (f + g)(x) = 2x² = 5x + 6, g(x) = x² + 8x - 7 (b) (f.g)(x) = x4 + 16x² + 256, g(x) = x² + 4x + 16 (c) (fog)(x) = (3x - 2)¹, g(x) = 3x - 2 (d) (gof)(x) = 18x - 25. g(x) = 6x - 7
Use the graph of y = f(x) to graph the given function g: g(x) = 2f(x)
Find (a) (f + g)(x), (b) (f – g)(x), (e) (f · g)(x), (4) (4) (x). What is the domain of (d)? 1) f(x) = 3x – 6, g(x) = 3 – x 2) f(x) =9(x) = x' +1 Evaluate the indicated function for f(x) = x² – 2 and g(x) = x – 1 algebraically. » )e - 2) 3) F – 9)(2) Find (a) (f • g)(x) and (b) (g • N(x) 5) f(x) = x* – 4, g(x) = Vx + 4 6) f(x) = x² + 9, g(x) = vF Use the graphs of f and g to evaluate the functions: 7)(a) (f – 9)(1) (b) (f - 9)(4) 8) (a) (f • g)(1) (b) (g • )(3) 8(x) y = f(x) y = g(x)
2) In words, communicate all transformations made on the parent function f(x) = 2* sketch the function: g(x) = -5-2-(x+1), +7
Please specify the answers
Look at the graphs of the function f(x)=x^2-1 and g(x) =x-1 What transformation makes g(x) greater than or equal to f(x) for -2 less than or equal to x and x less than or equal to 3? What transformation makes g(x) less than f(x) for all values of x?