**Plotting Constant Functions**

You may want to plot a constant, for instance to combine with another plot. To do this you specify the constant without a function and the domain within which you want to plot the function.

Plot[5, {x, 0, 5}]

Suppose you want to plot a constant x value for all y. That's not a function and Plot won't work. For instance, you may want to plot a vertical asymptote and while Mathematica will plot vertical asymptotes for some functions (see the plot for Tan@x in tutorial/Basic Plotting), it may not for all. Here is one method. Note that any number followed by pure Function "&" makes a constant Function for that number's value. In other words, the constant Function yields the constant no matter what number it is applied to.

4.5 & /@ {5, 28.6, Pi, E}

{4.5, 4.5, 4.5, 4.5}

Here we use the constant pure Function to create the x-values as just shown. Thread with List creates the 50 pairs of y-values for x = 7.

Thread[List[7 & /@ Range[0, 50], Range[0, 50]]] // Short

ListLinePlot[Thread[List[7 & /@ Range[0, 50], Range[0, 50]]]]

And so this is also a way to plot a constant y value by using the constant Function for the range instead of the domain.

ListLinePlot[Thread[List[Range[0, 50], 7 & /@ Range[0, 50]]]]

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