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Calculus/greatest integer function

Question
hello. How would you graph the following functions: f(x)=2[x], f(x)=[2x], f(x)=1/2[x], f(x)=[(1/2)x]. Also, what is the sol'n for the domain and range of y=(3x+5)/(x-2). Thanks

Unfortunately It is difficult to draw as this sight has no tools to draw with.
But [x] is the greatest integer function. Take a few different values of x say 1.6.
The greatest integer <= 1.6 is 1, so [1.6] = 1, and 2[1.6] = 2.

So all values of 2[x] where 1<=2 = 2 Plot on x y axes.

The domain is {x in R | x not = 2}

Find the inverse fn. x in terms of y.Swop x and y around and then it is easy to find the range.

Calculus

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mervyn

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I can solve problems in calculus, advanced calculus, differential and partial differential equations, complex variables, Fourier series and integrals, analysis,Gram-Schmidt orthogonalization, and Legendre polynomials. Soon I will be able to answer any question on advanced engineering control.

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Taught at university level

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Researching the Riemann Zeta Function Hypothesis