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.