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What is the range of #y=(-4x-3)/(x-2)#?

Answer 1

Nathan Axel

#f(x) = y = (-4x-3)/(x-2)#

#= ((-4x+8)-11)/(x-2)#

#= (-4(x-2)-11)/(x-2)#

#= -4-11/(x-2)#

#f(x)# can take any value except #-4# (to which #f(x)# is asymptotic as #x -> +- oo#).

So the range is #RR# \ #{-4}#

or in interval notation: #(-oo, -4) uu (-4, oo)#

graph{[-39.76, 39.8, -19.92, 19.83]} / (x-2)

More explicitly, we can express #x# in terms of #y# as

#x = 2-11/(y+4)#

which has an obvious excluded value at #y=4#

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Answer 2

Savannah Anderson

The range of y = (-4x - 3)/(x - 2) is all real numbers except for y = 4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.