Step 1

\(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{4}}}+{3}{x}^{{{3}}}-{x}+{1}\)

The leading coefficient is -1 (negative) and the degree is 4 (even)

Therefore \(\displaystyle{f{{\left({x}\right)}}}\rightarrow-\infty,{a}{s}\ {x}\rightarrow\infty\)

and \(\displaystyle{f{{\left({x}\right)}}}\rightarrow-\infty,{a}{s}\ {x}\rightarrow-\infty\)

Step 2

\(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{4}}}+{3}{x}^{{{3}}}-{x}+{1}\)

The leading coefficient is -1 (negative) and the degree is 4 (even)

Therefore \(\displaystyle{f{{\left({x}\right)}}}\rightarrow-\infty,{a}{s}\ {x}\rightarrow\infty\)

and \(\displaystyle{f{{\left({x}\right)}}}\rightarrow-\infty,{a}{s}\ {x}\rightarrow-\infty\)

Step 2