Case Study: Interpreting Wolfram Alpha's Graphical Output

A student inquired about the output to the input

parametric plot (sqrt(t+1), sqrt(t-1))

on Wolfram Alpha.
See the input and output here.

The first perplexing part of the output was the statement "(t from -1.78 to 1.78)." Most students will know that $t$ needs to be greater than or equal to 1.

Next, we can easily compute that at time $t=1$, we get the point $(\sqrt{2},0)$, but the picture doesn't look like it goes through this point.

After the student left, I realized from the labels that the graph were simply shifted.


As a remark, one can specify the range of the parameter. Enter the input

parametric plot (sqrt(t+1), sqrt(t-1)) t=1..2

.
See the input and output here.