They are NOT translations: they are TRANSFORMATIONS !
First transformation is the stretching of the coordinate plane along the y-axis with the coefficient of 3,
and then the shift of 2 units up.
It is possible to express EQUIVALENTLY in other terms: first is the compression along the x-axis
with the coefficient of 3 and then the shift of 2 units up.
Solved and explained.
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When you answer such questions, keep in your mind, that the sequence of the transformations DOES MATTER.
For example, in this case the stretching along y-axis followed translation along y-axis
IS NOT THE SAME as translation along y-axis followed stretching along y-axis.
Keeping it in your mind, re-consider the answer from @MathLover1, which is not precisely correct.
You can put this solution on YOUR website!
In the equation , the is acting as the or of the identity function, shifted up or down .
When is negative, there is also a vertical reflection of the graph.
Notice in the figure below that multiplying the equation of by the graph of by a factor of units if and the graph of f by a factor of units if . This means the larger the absolute value of , the steeper the slope.
in your case: the translation from to
graph is shifted up units
there is vertical stretch by a factor of units
