Home » Blog » Draw graphs of some step functions

Draw graphs of some step functions

Define a function

    \[ f(x) = \begin{cases} 1 & \text{for } 1 \leq x \leq 1; \\ 2 & \text{for } 1 < x \leq 2. \end{cases} \]

(The function is not defined if x < 0 or x > 2.)

  1. Graph of f.

    Rendered by QuickLaTeX.com

  2. Let g(x) = f(2x). Then the domain of g is all x such that 0 \leq x \leq 1. The graph is:

    Rendered by QuickLaTeX.com

  3. Let h(x) = f(x-2). Then the domain of h is all x such that 2 \leq x \leq 4. The graph is below.

    Rendered by QuickLaTeX.com

  4. Let k(x) = f(2x) + f(x-2). Then the domain is empty and so there is nothing to graph. (The domain is empty since f(2x) is only defined for 0 \leq x \leq 1 and f(x-2) is only defined for 2 \leq x \leq 4. There are no x that satisfy both of these conditions.)

One comment

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):