Diagram of the radio signals at different points in a superheterodyne radio receiver showing the problem of image response and why the receiver needs an RF image filter on the input.  The horizontal axis is frequency while the vertical axis is voltage.  The diagrams show what would happen in a superheterodyne without an RF filter.In the superheterodyne the signal of the desired radio station (S1, blue) at frequency fRF{\displaystyle f_{\text{RF}}} is mixed with a sinusoidal signal from a local oscillator (LO) at frequency fLO{\displaystyle f_{\text{LO}}}, producing a heterodyne or "beat" frequency at the difference between the two frequencies, called the intermediate frequency (IF) at fIF{\displaystyle f_{\text{IF}}}.  After being shifted to the intermediate frequency, the signal S1 passes through the IF filter which removes signals at all other frequencies, and is demodulated.    However there is a second frequency on the other side of the LO frequency which also produces a heterodyne at the IF frequency when mixed with the LO. This is called the image frequency fIMAGE{\displaystyle f_{\text{IMAGE}}}.  Thus the superheterodyne receives on two frequencies:  

fRF=fLO+fIF{\displaystyle f_{\text{RF}}=f_{\text{LO}}+f_{\text{IF}}\;}
fIMAGE=fLO−fIF{\displaystyle f_{\text{IMAGE}}=f_{\text{LO}}-f_{\text{IF}}\;}
If there happens to be a signal (S2, green) at the image frequency, it will also be shifted to the IF frequency, and pass through the IF filter along with the desired signal S1 (bottom graph), interfering with it.  Thus superheterodyne radios have a bandpass filter called the "RF filter" on the front end to remove any signals at the image frequency, to prevent interference.  The signal S2 is shown slightly displaced above the image frequency, so when shifted to the intermediate frequency it does not exactly coincide with the desired signal SI which would make the two signal difficult to distinguish on the graph.
Own work
Chetvorno