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junior college 1 | H2 Maths
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Hello. What does the +1 in the power do to the graph? Does it cause a steeper gradient? :)
Date Posted: 6 years ago
Views: 438
Recall your graph transformation.
e^x -> e^(x+1) translate to the left
e^(x+1) -> e^(2x+1) scale By factor of 1/2
e^x -> e^(x+1) translate to the left
e^(x+1) -> e^(2x+1) scale By factor of 1/2
Thanks!!
Alternatively you can use calculus. Differentiate your function and you'll realise that the constant in your index will not affect your gradient function at all.
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It's the factor 2 infront that changes the slope gradient. Not the +1.
Date Posted:
6 years ago
And yes, to the right, the graph becomes steeper. In other words, with the factor 2, y increases much faster than y=e^x. We can see this by taking derivative of y. y'=(2)e^(2x+1). To the left, as x is negative, the slope becomes more gentle.
Hmmm I don't think you can translate by 0.5 then scale by 0.5
You either
Translate by 1 then scale by .5
Or
Scale by 0.5 then translate by 0.5
You either
Translate by 1 then scale by .5
Or
Scale by 0.5 then translate by 0.5
Thank you so much, I understand this topic better now
The graph was poorly sketched Jiayang, good observation. In fact, there is no stretching at x=-0.5 as that's the new "zero" point. Both ways should give the same graph. But if squeeze by 0.5 first, than shifting should be -1, which is -0.5 in the original system. Haha... a bit confusing this way. So better do shifting first then stretching.
No problem Margaret, you will do well in this subject. Enjoy math.
When I said translate by 1 I was speaking loosely in absolute terms. What I was referring to was translate by one in the negative x direction but I was too lazy to type the whole thing
And no I don't think it's about your poorly sketched graph lool
The order drawn is top left, top right, bottom left then bottom right correct?
The order drawn is top left, top right, bottom left then bottom right correct?
Correct, that's the sequence.
But I think the difference is stretching from different "0" point. If translating by -1 first, stretching is wrt original system; but if translating by -0.5 first, stretching is wrt to the new "0" point. Both ways have to produce the same graph.
Ok understand you now. But were we taught this way in JC? I can't rmb :\
Ah... I did my pre-U in China Jiayang, even the syllabus was different. A-level covers much more.
I see... Yea I heard 高考 covers less breadth more depth than A levels
Hmmm... a lot of those "in dpeth" study becomes easy when we know calculus. Not sure which is better. Haha...
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