+73 4) Let f(x) = 1/x be the parent function. Let g(x) = (3x - 10)/(x - 4) be a transformation of f(x).
(a) Rewrite g(x) in the form a + (k/(x - 4)).
(b) Describe in words the transformations that take f(x) to g(x).
(c) If f(x) contains the points (-2, -½) and (1, 1), find the corresponding coordinates on g(x) using the transformation rules from part (b).
(d) Find the equations of the vertical and horizontal asymptotes.
(a) Rewrite g(x) in the form a+(k/(x-4))
I suppose that meant to simplify the division \(\frac{(3x-10)}{x-4}\)
\(Thus,3+\frac{2}{x-4}\) Same as the form.
+118677 Thanks guest, you made a good start. 
4) Let f(x) = 1/x be the parent function. Let g(x) = (3x - 10)/(x - 4) be a transformation of f(x).
a)
\(f(x)=\frac{1}{x}\qquad g(x)=\frac{3x-10}{x-4}\\~\\ g(x)=\frac{3x-10}{x-4}\\ g(x)=\frac{3x-12+2}{x-4}\\ g(x)=\frac{3(x-4)+2}{x-4}\\ g(x)=3+\frac{2}{x-4}\\ \)
Now let's look at this transformation
\(y=\frac{1}{x}\\ \text{If I translate the graph right (positive x direction) by 4 units I get }\\ y=\frac{1}{x+4}\\~\\ \text{If then translate the graph up 3 units i get }\\ y-3=\frac{1}{x+4}\\ y=3+\frac{1}{x+4}\\\)
(b) Describe in words the transformations that take f(x) to g(x).
So to transform f(x) to g(x) I must translate every point 4 units to the right and 3 units up.
(c) If f(x) contains the points (-2, -½) and (1, 1), find the corresponding coordinates on g(x) using the transformation rules from part (b).
\((-2,-0.5)\rightarrow (-2+4,-0.5+3)=(2,2.5)\)
Here is the graph:
https://www.desmos.com/calculator/gyqdgjfupu
(d) Find the equations of the vertical and horizontal asymptotes.
You should be able to finish the rest.
