Strang: Simple Calculus Question I'm looking at Gilbert Strang's introductory calculus textbook "Calculus".
https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf.
In chapter 1, fig 1.5, Strang illustrates what happens when you alter the function f(t) = 2t + 1. He shows the following equations along with two similar graphs, the second shifted downward.
f(t) = 2t + 1
f(t) - 2 = 2t - 1
I realize that taking the first equation and subtracting 2 from the RHS alone will nudge the graph down 2 tics, but he's done it to both sides. Shouldn't this result in the same function, and the same graph? My only guess is that maybe he forgot to  relabel the axes?
Screenshot: https://i.stack.imgur.com/HOtXF.png

Yes, when you write
$$f(t)-2=(2t+1)-2,$$ $f$ is still the same function.
But the author shows
$$g(t):=f(t)-2=2t-1$$ next to $f(t)$.

