One common technique used to discover the presence of an extrasolar planet around a star is to detect how they tug their stars about, creating small Doppler shifts in the stars' spectra.

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This is true. The Doppler shift method is one of the most common techniques used to detect exoplanets. As a planet orbits a star, it causes the star to wobble slightly, which can be detected through changes in the star's spectrum caused by the Doppler effect. By analyzing these changes, astronomers can infer the presence and properties of the planets orbiting the star.

One Common Technique Used to Discover the Presence of an Extrasolar