### Polynomials & Rational Functions

Building blocks

The function $a(x)=x+1$ can be combined in a number of ways with each of the functions $b(x)=2x-1, \quad b(x)=x^2-5x+8, \quad b(x)=x^2-5x-6$ to create a set of new functions. Can you find the correct one of graphs M to X to go in each cell of the grid below?
$\dfrac{1}{b(x)}$ $\dfrac{a(x)}{b(x)}$ $\dfrac{b(x)}{a(x)}$
$b(x)=$ $2x-1$
$b(x)=$ $x^2-5x+8$
$b(x)=$ $x^2-5x-6$