That will only happen if the modulating signal is limited at the input, i.e. if its amplitude will never exceed the maximum modulation index m=1. If so, then you get what's in the pictured. Or if you consider the strict mathematical formula, as @ThePhoton says in his comment (just added). Else, the carrier will try to accomodate the excess by phase inversion:
The first (bottom) trace shows a modulation of 0.5, for the middle one m=1, and the top one m=1.5. Note the phase inversion that happens at ~0.4s. Fromhere on, the carrier will only change in amplitude, having the same inversion. Usually, the signal is limited to less than m=1, for good reasons.
Here's the FFT of each modulation:
The black trace is with m=0.5, it shows two peaks, symmetric over 10Hz (the carrier), 1Hz apart (input). The blue trace shows the same two peaks, twice as big, for m=1 (of course...).
Corection: For m=-1.5, there are even larger sidelobes. But the detection can not be done now because the peaks suggest the modulation input is folded where the negative m is.
In addition, heres how it looks when the input is limited to \$\pm\$1, but m=1.5: