Question

Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls see pic for details

Answer 1

c.

The line equation is of the form

`y=mx+c\ldots(1)`

From the graph, we observe and find these points

(1,5) and (0,4) lie on the given line.

Substituting x=1, y=5 in equation (1), we get

`5=m(1)+c`

`m+c=5\ldots\text{.}(2)`

Substituting x=0, y=4 in equation (1), we get

`4=m(0)+c`

`c=4`

Substituting c=4 in equation (2), we get

`m+4=5`

`m=5-4`

`m=1`

Substituting c=4,m=1 in equation (1), we get

`y=x+5`

We need to write this equation in the form of r(x) = p(x) / q(x).

`r(x)=(p(x))/(q(x))\ldots(3)`

Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get

`x+5=(p(x))/(x)`

Using the cross-product method, we get

`x(x+5)=p(x)`

`x* x+x*5=p(x)`

`x^2+5x=p(x)`

Substitute values in equation (3), we get

`x+5=(x^2+5x)/(x)`

Hence the required equation is

`x+5=(x^2+5x)/(x)`