8(b+1)=-3(2+b) simply
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We start with the parent function
The first child function would be
We have multiplied the input of the function by a constant: we have
This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.
The second child function would be
We added 6 to the input of the function: we have
This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.
The third child function would be
We changed the sign of the previous function (i.e. we multiplied it by -1): we have
This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.
The fourth child function would be
We added 3 to previous function: we have
This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.
Recap
Starting from the parent function , we have to:
- Compress the graph horizontall, with scale factor 2;
- Translate the graph 6 units to the left;
- Reflect the graph across the x axis;
- Translate the graph 3 units up
Note that the order is important!