The bandwidth in octaves around the center frequency is preserved when dragging the center frequency. If neither the upper or lower frequency limits are defined, then the full frequency range is selected, just like a 'normal' audio selection. If, instead, the selection is dragged up to the top of the track, then the high frequency will be undefined, so the selection will include everything above the low frequency limit. The high frequency selection is about 5,000 Hz and the low frequency selection is not defined, so the selection includes everything below 5,000 Hz: In the illustration below, the selection has been dragged from about 5,000 Hz to the bottom of the track. If either the low or high frequency limits are not defined, no center frequency will be shown. The center line will be visually centered in Logarithmic scale.

Thus if as in the above image the Spectrogram scale is set to the default 'Linear' choice (using Spectrograms Preferences or the track's Spectrogram Settings in the Audio Track Dropdown Menu), the center line will appear below the visual center of the frequency range.

The center frequency is proportionally in the center and is a geometric mean (which is appropriate for filtering purposes) rather than an arithmetic mean.

Frequency shifter audacity