Question 954426
{{{(x-4)^2 / 4 -(y+3)^2 / 9 = 1}}} -this is a hyperbola

  Hyperbolas CAN be functions, but NOT all hyperbolas are functions. The ones that are NOT functions are in the form of {{{x^2/a^2 - y^2/b^2 = 1}}}. Whenever {{{y}}} is squared, you do {{{not}}} have a functions.

The Vertical Line Test is also helpful:
The test states that a graph represents a function if and only if all vertical lines intersect the graph at {{{most}}} once. 

{{{drawing( 600, 600, -10, 15, -15, 15,
line(-2,15,-2,-15),line(6.5,15,6.5,-15),line(-1,15,-1,-15),line(8,15,8,-15),
 graph( 600, 600, -10, 15, -15, 15, sqrt(((x-4)^2 / 4 - 1)9)-3, -sqrt(((x-4)^2 / 4 - 1)9)-3)) }}}