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?

The graphs are available as cards to print out, along with a large format grid.

\(a(x)=\) \(x+1\) | \(\dfrac{1}{b(x)}\) | \(\dfrac{a(x)}{b(x)}\) | \(\dfrac{b(x)}{a(x)}\) |
---|---|---|---|

\(b(x)=\) \(2x-1\) | |||

\(b(x)=\) \(x^2-5x+8\) | |||

\(b(x)=\) \(x^2-5x-6\) |