Question

In which order should transformations of f(x) be performed? I know translations come last and stretched usualyl come first, but what do you do when the transformation contains an absolute value or a recpirocal?

Answer 1

wen it contains an absolute value, u just reflect wat ever is below the x-axis,about the x-axis.(since absolute value gives no negative value)(dat is wy wen u hav |x|, the x>0 part remains so.but x<0 part gets reflected about the x-axis)
wen it is reciproca: usual nothing much can be predicted...except the fact of wer it'll go to infinity.

Answer 2

agree on the absolute value.

so example f(x)=|-3x+2|
we only take positive values.
all negative values become positive by multiplying by -1, hence the reflection about the x axis spoken about by brackett.

for reciprocals example:
f(x)=1/x-2
we have to be careful about what values the denominator can take.
here x cannot equal 2 as we cannot divide by zero.

f(x) as x becomes large so does x-2, so 1/x-2 becomes small.
and vice versa as x becomes small, 1/x-2 becomes large.