# Graph the polynomial function. f(x)=x^{5}+x

Question
Polynomial graphs
Graph the polynomial function.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{5}}}+{x}$$

2020-12-31
Step 1
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{5}}}+{x}$$
The leading coefficient is 1 (positive) and the degree is 5 (odd)
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

### Relevant Questions

Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}$$
Graph each polynomial function. Factor first if the expression is not in factored form.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$
Graph each polynomial function. Factor first if the expression is not in factored form.
$$\displaystyle{f{{\left({x}\right)}}}={\left({3}{x}-{1}\right)}{\left({x}+{2}\right)}^{{{2}}}$$
Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}+{3}\right)}{\left({x}+{2}\right)}^{{{2}}}$$
Graph each polynomial function. Factor first if the expression is not in factored form. PSKf(x)=x^{3}\ +\ 3x^{2}\ -\ 13x\ -\ 15 PSZ
Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{4}{x}^{{{3}}}-{5}{x}^{{{2}}}+{14}{x}-{15}$$
Rational functions can have any polynomial in the numerator and denominator. Analyse the key features of each function and sketch its graph. Describe the common features of the graphs. $$\displaystyle{a}{)}{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}^{{{2}}}-{1}}}}\ {b}{)}{g{{\left({x}\right)}}}={\frac{{{x}-{2}}}{{{x}^{{{2}}}+{3}{x}+{2}}}}\ {c}{)}{h}{\left({x}\right)}={\frac{{{x}+{5}}}{{{x}^{{{2}}}-{x}-{12}}}}$$
a) Identify the parameters a, b, h, and k in the polynomial $$\displaystyle{y}={\frac{{{1}}}{{{3}}}}{\left({x}+{3}\right)}^{{{3}}}-{2}$$ Describe how each parameter transforms the base function $$\displaystyle{y}={x}^{{{3}}}$$.
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}^{{{2}}}−{4}\right)}{\left({x}−{1}\right)}$$
Graph the polynomial function. $$\displaystyle{f{{\left({x}\right)}}}=−{x}^{{{4}}}+{3}{x}^{{{3}}}−{x}+{1}$$