Transformations. Use a sequence of transformations, starting from the reciprocal function y=1/x to graph the rational function

Question

Transformations. Use a sequence of transformations, starting from the reciprocal function y=1/x to graph the rational function

r(x) = 4x+3/2x+1

Show each graph in the sequence and describe each transformation.

Hint: use long division to write r(x) as a quotient plus proper rational function, r(x) = A + B / 2x + 1

Answer 1

For the specific problem you do not even have to perform the long division.

Notice that ( 4x +3 ) / (2 x+ 1 ) = ( 4x +2 +1 ) / (2 x+ 1 ) = [ 2( 2 x+ 1 ) +1 ] / (2 x+ 1 )

= 2( 2 x+ 1 ) / (2 x+ 1 ) + 1 / (2 x+ 1 ) = 2 + (1/2) [ 1 /( x +1 /2) .

Now the ball is in your court