Leave explanation. The graph of the function $ f(x) = \frac{1}{x + 4} - 13 $ is a transformation of the graph of the function $ g(x) = \frac{1}{x} $ by:- A horizontal shift of _____ units.- A vertical shift of _____ units.

Answered: The graph of the fur A vertical sh A…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Leave explanation.

The graph of the function $ f(x) = \frac{1}{x + 4} - 13 $ is a transformation of the graph of the function $ g(x) = \frac{1}{x} $ by:

- A horizontal shift of _____ units.
- A vertical shift of _____ units.

Expert Solution

Step 1

Vertical shift and horizontal shift:

A new function $g (x) = f (x) + k$ , where k may be a constant, may be a vertical shift of the function $f (x)$ , given a function $f (x)$ . All of the output values are adjusted by k units. The graph will move up if k is positive and will move down if k is negative.
Given a function f, a brand new function $g (x) = f (x - h)$ could be a horizontal shift of the function f, where h could be a constant. The graph will move right if h is positive and shift left if h is negative.