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S_A_V [24]
3 years ago
10

Polygons EFHG and E′F′H′G′ are shown on the following coordinate grid: A coordinate grid is shown from positive 6 to negative 6

on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon EFHG is shown with vertex E on ordered pair 2, 2, vertex F on ordered pair 2, 4, vertex H on ordered pair 3, 5 and vertex G on ordered pair 3, 1. A polygon E prime F prime H prime G prime is shown with vertex E prime on ordered pair negative 1, 2, vertex F prime on ordered pair negative 3, 2, vertex H prime on ordered pair negative 4, 3, and vertex G prime on ordered pair 0, 3. What set of transformations is performed on EFHG to form E′F′H′G′?

Mathematics
1 answer:
stira [4]3 years ago
6 0
Check the first picture. Our goal is to map  <span>EFHG to  E′F′H′G′.
</span>
All choices involve a rotation by 90° or 270°<span> counterclockwise about the origin.

consider a rotation </span>by 90° counterclockwise. Each point P(a, b) can be rotated 90° cwise about the origin to form P"(a",b") :

by drawing the right angle POP", such that |PO|=|OP"|.

or by plotting each P"(a",b") so that  (a",b")=(-b, a)

for example if G(3, 1) is mapped to G(-1, 3) by either of the procedures described.

check picture 2.

EFHG  is mapped to E′'F'′H'′G′'.

In order to map E′'F'′H'′G′' to E'F′H'G′, we need to translate the figure 1 unit right.


Answer: 

"<span>A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right</span>"

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dsp73

Given:

The two functions are:

f(x)=4^x

g(x)=4^x+2

To find:

The type of transformation from f(x) to g(x) in the problem above and including its distance moved.

Solution:

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  • If a>0, then the graph shifts a units left.
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We have,

f(x)=4^x

g(x)=4^x+2

The function g(x) can be written as

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On comparing (i) and (ii), we get

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