Question

Question #618a7

Answer 1

You can't

Explanation:

To graph this function starting with `1/x`, first we need to write it in the form:
`y=a+b/(x+c)`

Given:

`y=(2x+3)/(5x-1)`

`y=2/5times(x+3/2)/(x-1/5)`

`y=2/5times(x-1/5+1/5+3/2)/(x-1/5)`

`y=2/5times((x-1/5)/(x-1/5)+(17/10)/(x-1/5))`

`y=2/5times(1+(17/10)/(x-1/5))`

`y=2/5+(34/25)/(x-1/5)`

As you can see, the denominator can't be in the form of just `x`.

To graph the function starting with `f(x)=1/x`

graph{1/x [-5, 5, -5, 5]}

We do the following transformations:

1) Shift `1/5` to the right:
`f(x-1/5)=1/(x-1/5)`

graph{1/(x-1/5) [-5, 5, -5, 5]}

2) Stretch vertically by a factor of `34/25`:
`34/25timesf(x-1/5)=(34/25)/(x-1/5)`

graph{(34/25)/(x-1/5) [-5, 5, -5, 5]}

3) Shift `2/5` up to get the final graph:
`34/25timesf(x-1/5)+2/5=2/5+(34/25)/(x-1/5)`

graph{(34/25)/(x-1/5)+2/5 [-5, 5, -5, 5]}