Which function has an inverse?
a)
f(x) = x2 + 3, x51
b)
f(x) = x2 + 8x - 9, x5-6
f(x) = 2x2 + 8x-4, xs-2
d)
f(x) = 2x2 - 4x + 1, x23

-1   1/6.   you dont subtract the denominators

step-by-step explanation:

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.