#Trig Graph, please help me

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prime heart
timber moatBOT
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desert flare
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how much do you know about transformations?

prime heart
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I get the basics

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Actually AI gave me this response:
Transformations:
(a) The function f(x) = 4 sin(2x - π/2) + 2 is obtained by performing the following transformations on f(x) = sin(x):
Horizontal compression by a factor of 1/2 (replacing x with 2x)
Horizontal shift to the right by π/2 (replacing x with x - π/2)
Vertical stretch by a factor of 4 (multiplying sin(x) by 4)
Vertical shift upwards by 2 (adding 2 to sin(x))

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Is this right or way off

desert flare
prime heart
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It's worked before

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Is it way off

desert flare
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it’s impressively close

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off on the horizontal shift/translation, as it would be

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that’s generally the hardest part

prime heart
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I think MetaAI is a bit better with numbers than ChatGPT

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But anyways, how can I start answering this question?

desert flare
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i would factor 2x - π/2 into 2(x - π/4)

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since this allows you to see that the function, at some point, “replaces” x with x-π/4

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(as opposed to x-π/2)

prime heart
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@desert flare

desert flare
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now start by identifying dilations

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remember that replacing x with ax is a horizontal scale factor of 1/a (i.e. for a>1, the graph is narrowed), and replacing f(x) with af(x) is a vertical scale factor of a (i.e. normal and what you’d expect)

prime heart
desert flare
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nice

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now the translations

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horizontal translation of a to the right will replace x with x-a

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vertical translation of a up will replace f(x) with f(x) + a

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(left and down are just what happens when a is negative)

prime heart
desert flare
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that’s basically it for (a)

prime heart
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sweet

desert flare
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did you want to give part (b) a try yourself first?

prime heart
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How should I start

desert flare
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the y-intercept is usually easier to find

prime heart
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x=0 yeah

prime heart
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yo @desert flare

desert flare
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hi sorry i was afk

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y-intercept looks accurate

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now try x-intercepts

prime heart
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@desert flare this is my friends answer

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it's different right

desert flare
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your friend also claims that the horizontal translation is π/2

prime heart
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he is pretty smart

desert flare
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and, unsurprisingly, i am of the opinion that i am correct