Need Help Writing Equations For These Equations? Pre Calc 12 Need Help Writing Equations For These Equations? Pre Calc 12
1) Vertical Asypmptotes at x=1/4, x intercept of x=0, and a discontinous point at (5,5/19)
2) Y-Intercept at -5, no x-intercepts, discontinous points at (-1,-5) and (3,-5) 
 A: I'll do some trouble-shooting with respect to the first question: 
$(1)$ For the first, we need that it intersects the $x-axis$ (i.e. y = 0) when $x = 0$. So when $x = 0 \implies y = 0$: the function must intersect the origin. You need to do a little trial-and-error: how would a rational function have a vertical asymptote at $x = 1/4$? Often case, this is when the denominator evaluates to $0$ when $x = a$, where $x = a$ is a vertical asymptote.  So: try $$y = \dfrac x{4x-1}$$
Note: $4x - 1 = 0 \iff x = 1/4$. Note that the point $x = 0 \implies y = 0$, which  satisfies the y-intercept at $x = 0$.
Now, how can we make the function discontinuous at $\left(5, \frac 5{19}\right)$?

$(2)$: Hint...Consider the equation of the horizontal line $y = -5$; it certainly intersects the y-axis when $x = 0$ and figure out how you can modify /define the function to make it discontinuous when $x = -1, x = 3$: recall, you can define a function to be a *piece-wise" function: E.g., figure out the x-values that will make the second function discontinuous at the required points:
$$y = \begin{cases} 11 & \text{when}\;\;x = a \;\text{or}\;x = b \\ \\
-5 & \text{otherwise}
\end{cases}
$$
Why don't you work at this, and work some more on $(1)$, and comment below with any progress report.
