data={{0,0.5},{1,0.7},{2,1.6},{3,2.6},{4,3.4},{5,4.8},{6,5.6},{7,6.8}};

line = Fit[data, {1,x},x]

parabola= Fit[data, {1,x,x^2},x]

quartic=Fit[data, {1,x,x^2,x^3,x^4},x]

Show[ListPlot[data, PlotStyle->Red],
 Plot[{line,parabola,quartic}, {x, 0, 7},PlotStyle->{Orange,Brown,Blue}],
AspectRatio->1]

f[x_]=quartic

Map[f,{0,1,2,3,4,5,6,7}]