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Another question about domains and range
how would I find the range of (3x-4)/(6x-1) ? Without using a graph

the domain is x can't be 1/6

What is the range?

  • Algebra -

    without using a graph

  • Algebra -

    The range is how high or how low your graph can go
    So look at what happens when you use large values of x
    e.g. in your mind try x = 100 000
    so you would have 299 996/599 999
    For all practical purposes this is 3/6 or 1/2, even though you will never reach it.
    As a matter of fact try it on your calculator you will get .49999... , in other words, less than 1/2
    The larger the value of x, the closer we will get to 1/2

    If we try large negative values of x
    say, x = -100 000
    then our calculation is -300 006/-600 001
    which is slightly over .5

    so no value of x will produce a y equal to 1/2

    so the domain is the set of all real values of y ,except y = .5

    (if you try to solve
    (3x-4)/(6x-1) = 1/2
    we get
    6x - 8 = 6x-1
    -8 = -1 which is false and a contradiction.
    So there is no solution)

  • Algebra -

    1. Use a calculator to approximate the square root of 320. Round to three decimal places

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