The transformation of a function f(x) into a function g(a) is given by g(a) = Af(Bx + H) + K.where the constants• A vertically scales the function. (negative A reflects the function about the x-axis.)• B horizontally scales the function. (negative B reflects the function about the y-axis.)• H horizontally shifts the function.• K vertically shifts the function.Transform f(x) into g(z) where the transformation is g(a) = f(# – 1) + 3The function f(E) is shown below in red. Graph the transformed function g(z) by first placing a dot at eachend point of the new transformed function and then click on the "line segment" button and connect the twoblue dots.(Hint: Transform the function by applying the constants in this order: H, B, A, K.)2-6 -5 -4 -3 -2 -11 2 3 4 5 6-2-3-4-5Clear All Draw: DotLine SegmentCheck Answer

Answered: %3D The transformation of a function…

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

Concept explainers

Question

The transformation of a function f(x) into a function g(a) is given by g(a) = Af(Bx + H) + K.
where the constants
• A vertically scales the function. (negative A reflects the function about the x-axis.)
• B horizontally scales the function. (negative B reflects the function about the y-axis.)
• H horizontally shifts the function.
• K vertically shifts the function.
Transform f(x) into g(z) where the transformation is g(a) = f(# – 1) + 3
The function f(E) is shown below in red. Graph the transformed function g(z) by first placing a dot at each
end point of the new transformed function and then click on the "line segment" button and connect the two
blue dots.
(Hint: Transform the function by applying the constants in this order: H, B, A, K.)
2
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
-2
-3
-4
-5
Clear All Draw: Dot
Line Segment
Check Answer

Expert Solution

Step 1

Given function is $g (x) = f (x - 1) + 3$ .

Comparing the function $g (x)$ with $A f (B x + H) + K$ , we obtain the following.

$\begin{array}{rcl} A & = & 1 \\ B & = & 1 \\ H & = & - 1 \\ K & = & 3 \end{array}$ .

Vertical scaling: $k f (x)$ vertically scales the graph in y-axis (k>1 stretches the graph, 0<k<1 shrinks the graph vertically).

Horizontal scaling: $f (k x)$ Horizontally scales the graph in x-axis (k>1 shrinks the graph, 0<k<1 stretches the graph).

As $A = 1$ there is no vertical scaling from the definition.

And as B=1 there is no horizontal scaling from the definition.

Horizontal shift: Shifts the function horizontally $f (x + H)$ , if H>0 the function shifts right sided of x-axis, H<0 the function shifts left of x-axis.

Vertical shift: Shifts the function vertically $f (x) + k$ , if k>0 the function shifts above y-axis, k<0 the function shifts below y-axis.

As H=-1 horizontally shifts the function. That is function is shifted to left side of x-axis.

K=3 vertically shifts the function. That is function is shifted above y- axis .

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Functions and Inverse Functions$

Learn more about

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

Similar questions