Two functions are given that, first is \(\displaystyle{y}={e}^{{{x}}}\) and anotheris \(\displaystyle{y}={1}+{x}+{\frac{{{x}^{{{2}}}}}{{{2}}}}+{\frac{{{x}^{{{3}}}}}{{{6}}}}+{\frac{{{x}^{{{4}}}}}{{{24}}}}\).

The graph of exponential functional \(\displaystyle{y}={e}^{{{x}}}\) is:

The graph of polynomial functional \(\displaystyle{y}={1}+{x}+{\frac{{{x}^{{{2}}}}}{{{2}}}}+{\frac{{{x}^{{{3}}}}}{{{6}}}}+{\frac{{{x}^{{{4}}}}}{{{24}}}}\)..

The graphs of both functions in the same viewing rectangle are:

The graph of exponential functional \(\displaystyle{y}={e}^{{{x}}}\) is:

The graph of polynomial functional \(\displaystyle{y}={1}+{x}+{\frac{{{x}^{{{2}}}}}{{{2}}}}+{\frac{{{x}^{{{3}}}}}{{{6}}}}+{\frac{{{x}^{{{4}}}}}{{{24}}}}\)..

The graphs of both functions in the same viewing rectangle are: