Plus construction is functorial

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Given a nice map (cellular map) $f : X\rightarrow Y$ between CW complexes $X$ and $Y$, how is $f^{+}$ defined between their plus constructions?

Going through my old notes, I've learnt that the plus construction is functorial, i.e., $f^{+}$ is well defined because $\pi_1$ is functorial, but I'm not able to see how. (Its been a long time)

Also, if $f$ and $g$ are homotopic cellular maps, are $f^{+}$ and $g^{+}$ homotopic?

Are there any good references for this?