Why was "tantrum" trending last week?
1890, "capable of being influenced," from suggest + -ible. Meaning "that can be suggested" is from 1905.
suggestibility sug·gest·i·bil·i·ty (səg-jěs'tə-bĭl'ĭ-tē, sə-jěs'-)n. Responsiveness or susceptibility to suggestion.
suggestible sug·gest·i·ble (səg-jěs'tə-bəl, sə-jěs'-)adj. Readily influenced by suggestion.