Table 2: Fits to the local and distant K-band TFRs, using $M_K({\rm AB})=a+b\times \log{(V_{\rm flat})}$ .
K-band TFR Slope a Zero point b Comments

Local relation $-6.88 \pm 0.57$ $-6.54 \pm 1.33$ SDSS subsample

Distant RDs -6.88 $-5.88\pm0.09$ Using local slope

Distant RDs $-7.24\pm1.04$ $-5.07\pm2.37$ Slope free

Distant RD/RD+ -6.88 $-5.92 \pm 0.10$ Using local slope

Distant RD/RD+ $-6.47 \pm 1.30$ $-6.85 \pm 2.98$ Slope free

**Table 2:** Fits to the local and distant K-band TFRs, using $M_K({\rm AB})=a+b\times \log{(V_{\rm flat})}$ .
K-band TFR	Slope a	Zero point b	Comments
Local relation	$-6.88 \pm 0.57$	$-6.54 \pm 1.33$	SDSS subsample
Distant RDs	-6.88	$-5.88\pm0.09$	Using local slope
Distant RDs	$-7.24\pm1.04$	$-5.07\pm2.37$	Slope free
Distant RD/RD+	-6.88	$-5.92 \pm 0.10$	Using local slope
Distant RD/RD+	$-6.47 \pm 1.30$	$-6.85 \pm 2.98$	Slope free

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