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

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RASTA

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20:59 Uhr, 09.01.2022

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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)=2x is reflected over the x-aξs 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




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pivot

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23:25 Uhr, 09.01.2022

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Hi,

to reflect (x)=2x on the x-axis you just multiply f(x) by (-1). Thus the reflected function is fr(x)=-2x

To shift fr(x) to the right you subtract 3 from the x-variable: g(x)=-2(x-3)=-2x+6

greetings,
pivot
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supporter

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07:33 Uhr, 10.01.2022

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

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15:37 Uhr, 13.01.2022

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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

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02:33 Uhr, 16.01.2022

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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.
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pivot

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18:02 Uhr, 17.01.2022

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Let´s say the linear function is f(x)=mx+b. Now you reflect it at the x-axis. For this purpose you just multiply the function by -1: fr(x)=-mx-b.
If then the function is translated d units to the right you subtract d from x : g(x)=-m(x-d)-b=-mx+md-b
If then the function is translated d units to the left you add d to x: g(x)=-m(x+d)-b=-mx-md-b

numerical example: f(x)=3x+5
Reflecting f(x) at the x-axis and then translate the reflected function two units to the left.

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

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RASTA

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15:34 Uhr, 22.01.2022

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

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15:49 Uhr, 22.01.2022

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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.