Question

How do you graph `y=(34x-2)/(16x+4)` using asymptotes, intercepts, end behavior?

Answer 1

I have managed to present the rectangular hyperbola represented by your equation.. Vertical asymptote: `x =-1/4`; the horizontal one: `y = 17/2`. See explanation, for more.

Explanation:

graph{(y-17/2) (x+1/4)+9/4=0 [-40, 40, -20, 20]}

By actual division and reorganization,

`(y-17/2)(x+1/4)=-9/4`

This represents athe rectangular hyperbola with asymptotes #y

=17/2 and x = -1/4#.

The center is at the common point `(-1/4, 17/2)`..

The graph would clarify these statements.

As `y to 17/2, x to +-oo`.

As `x to -1/4, y to +-oo`.

Not easy to see in the graph, the x-intercept is 1/68 and y-intercept

is `-`1/2.

Note that the general equation of a rectangular hyperbola is of the

form

`(y-mx+a)(x+my+b) = c`,

enabling us to read the equations of the asymptotes as

`y -mx + a =0=x+my+b`