how to draw inverse functions? (1 Viewer)

malcolm21 · Aug 6, 2015

i dont know where to start the line, from the right side or left side so i get it reversed sometimes

Drsoccerball · Aug 6, 2015

malcolm21 · Aug 6, 2015

like

starts from the bottom left and goes upwards in the shape but sometimes the curve starts from the right and goes up, i dont know where to start it

leehuan · Aug 6, 2015

That is not a technical way of putting it....

However

If you look at the basic curves, y=sin^-1(x) and y=tan^-1(x) are increasing
y=cos^-1(x) is decreasing

Obviously if you chuck a negative sign in front of either it goes the other way around.

InteGrand · Aug 6, 2015

malcolm21 said:
like

starts from the bottom left and goes upwards in the shape but sometimes the curve starts from the right and goes up, i dont know where to start it

That would only start from the right if there was a minus sign in front of the 2 (or equivalently, inside the brackets, since the inverse sine function is an odd function).

Using our knowledge of how to sketch related graphs from a known graph, we sketch the given function by:

• first sketching $y=\sin ^{-1}x$

• then dilating it horizontally by a factor of 3 to get the graph of $y=\sin ^{-1} \frac{x}{3}$

• then stretching our graph of $y=\sin ^{-1} \frac{x}{3}$ horizontally by a factor of 2 to get the graph of $y=2\sin ^{-1} \frac{x}{3}$ .

(Nowhere in this process was our graph flipped in any way, so its orientation is the same as the graph of $y=\sin^{-1}x$ .

Also, you should get a few key points down (the endpoints and the 'middle' of the graph) with a table of values to assist the sketching.

kawaiipotato · Aug 7, 2015

You should first know what sin^-1 x and cos^ -1 x looks like already.
Then for sine inverse: $y = asin^{-1}(bx) + x_{0}$

$$ Step 1. $ Domain: -1 \leq bx \leq 1$

$\frac{-1}{b} \leq x \leq \frac{1}{b}$

$$ Step 2. $ Range: \frac{-\pi}{2} \leq sin^( $linear $) \leq \frac{\pi}{2}$

$a* \frac{- \pi}{2} \leq asin($linear$) \leq a* \frac{\pi}{2}$

$Mark all these extreme points (for both range and domain)$ $Remember that the POI occurs in the middle of your range$

$Step 3. $ $ Sub in an extreme point (x coordinates on the borders of domain) to see where it starts at that point $ $ Then just follow the trend that the $ y = sin^{-1}x $ curve follows until your reaching your other extreme point$

$$ You can extend the thing inside the sine inverse bracket $ $ to a full linear, such as $ sin^{-1}\frac{bx+c}{d}$

how to draw inverse functions? (1 Viewer)

malcolm21

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Drsoccerball

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malcolm21

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leehuan

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InteGrand

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kawaiipotato

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