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What is the equation for the graph of g(x)g left p

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Tags: Mathematik

RASTA aktiv_icon

20:59 Uhr, 09.01.2022

Tag!
I need you point me in the right direction here. where to focus my attention first. thank you in advance for your help!

The graph of the equation

f (x) = 2 x

is reflected over the

x - a ξ s

and translated three units to the right to become g(x)gas depicted below.

What is the equation for the graph of

g (x) g

Für alle, die mir helfen möchten (automatisch von OnlineMathe generiert):
"Ich möchte die Lösung in Zusammenarbeit mit anderen erstellen."

pivot aktiv_icon

23:25 Uhr, 09.01.2022

Hi,

to reflect

(x) = 2 x

on the x-axis you just multiply

f (x)

(- 1)

. Thus the reflected function is

f_{r} (x) = - 2 x

To shift

f_{r} (x)

to the right you subtract

3

from the

x

-variable:

g (x) = - 2 (x - 3) = - 2 x + 6

greetings,
pivot

supporter aktiv_icon

07:33 Uhr, 10.01.2022

www.wolframalpha.com/input/?i=plot+-2x+%2C+-2%28x-3%29

RASTA aktiv_icon

15:37 Uhr, 13.01.2022

thank you both. I have not forgotten about the question.

i

am just studying the topic. it is kind of new to me. I study math on my own and with textbooks. Don't go to school. I work. So I am sort of pressed for time. Thank you for the tips. I am studying everything about graph transformation and all that. I will get back if in doubt.

RASTA aktiv_icon

02:33 Uhr, 16.01.2022

Tag, if

i

didn't reply was because

i

was studying the topic. it is a new one for me

i

input all the equations given in the answer choice and was clear for me to see that choice

A (

the first one) was the right equation.

Now, I would like to know how to do it without the graphing calculator. pivot, can you explain the reasoning behind what you wrote. I do not understand it well. thank you so much.

pivot aktiv_icon

18:02 Uhr, 17.01.2022

Let´s say the linear function is

f (x) = m x + b

. Now you reflect it at the x-axis. For this purpose you just multiply the function by

- 1

f_{r} (x) = - m x - b

\cdot

If then the function is translated

d

units to the right you subtract

d

from

x

g (x) = - m (x - d) - b = - m x + m d - b

\cdot

If then the function is translated

d

units to the left you add

d

x

g (x) = - m (x + d) - b = - m x - m d - b

numerical example:

f (x) = 3 x + 5

Reflecting f(x) at the x-axis and then translate the reflected function two units to the left.

f_{r} (x) = - 3 x - 5

g (x) = - 3 (x + 2) - 5 = - 3 x - 11

RASTA aktiv_icon

15:34 Uhr, 22.01.2022

thank you so much. Ich verstehe jetzt. I have also been watching some tutorials and videos about graphing transformation of exponential equations.

pivot aktiv_icon

15:49 Uhr, 22.01.2022

Freut mich, dass das klar ist. Transformationen von Exponentialfunktionen sind natürlich was anderes. If something unclear about that issue, feel free to ask a new question.

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