Transformations on rational functions where x is in the numerator and denomiator.

Question

The problem was to plot $ f(x) = \frac{x-2}{x-1} $ using transformations.

There are samples and videos online on transforming simpler rational functions like:

$$ y = \frac{1}{x} $$

and that easy to understand. But nothing this complex.

In this case, though, what is the parent function to transform from?

How does one even start with this?

Notice that $f(x)=1-\frac{1}{x-1}$ – Kal S. Dec 30 '13 at 01:18 — Kal S., Dec 30 '13 at 01:18
@anorton I wrote it as an answer, thank you. – Kal S. Dec 30 '13 at 02:20 — Kal S., Dec 30 '13 at 02:20

score 3 · Accepted Answer · answered Dec 30 '13 at 02:18

3

Hint: Notice that $f(x)=1-\frac{1}{x-1}$. Then starting from $y=\frac{1}{x}$ the first transformation moves the graph along x-axis and the second moves the graph along the y-axis.

answered Dec 30 '13 at 02:18

Kal S.

3,781

To sum up, $$ y = \frac{1}{x} $$ is, in fact, the parent function. – Marty B. Dec 30 '13 at 11:27

score 0 · Answer 2 · answered Dec 30 '13 at 05:47

In addition, the following is a breakdown of the operartions involved:-

Let $f(x) = \frac{1}{x}$.

f(x) is transformed to g(x) where g(x) = f(x – 1). [= Right shifting f(x) by 1 unit]

g(x) is then transformed to h(x) where h(x) = –g(x). [= reflecting g(x) about the x-axis]

h(x) is then transformed to k(x) where k(x) = 1 + h(x). [= Up shifting h(x) by 1 unit.]

Transformations on rational functions where x is in the numerator and denomiator.

2 Answers2