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Draw the graphs of some step functions

For all x \in \mathbb{R} define

    \[ f(x) = [x], \qquad g(x) = [2x] \]

where [x] denotes the greatest integer less than or equal to x. Draw the function h(x) for each of the following on the interval [-1,2]:

  1. h(x) = f(x) + g(x).
  2. h(x) = f(x) + g\left(\frac{x}{2} \right).
  3. h(x) = f(x) g(x).
  4. h(x) = \frac{1}{4} f(x) g(x).

    1. Graph of h(x) = f(x) + g(x) = [x]+[2x].

      Rendered by QuickLaTeX.com

    2. Graph of h(x) = f(x) + g\left(\frac{x}{2}\right) = [x] + [x] = 2[x].

      Rendered by QuickLaTeX.com

    3. The graph of h(x) = f(x)g(x) = [x]\cdot[2x].

      Rendered by QuickLaTeX.com

    4. The graph of h(x) = \frac{1}{4}f(x)g(x) = \frac{1}{4}[x][2x].

      Rendered by QuickLaTeX.com

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