Graph the polynomial function. f(x)=−x^{4}+3x^{3}−x+1

Question
Polynomial graphs
asked 2021-02-25
Graph the polynomial function. \(\displaystyle{f{{\left({x}\right)}}}=−{x}^{{{4}}}+{3}{x}^{{{3}}}−{x}+{1}\)

Answers (1)

2021-02-26
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 image
0

Relevant Questions

asked 2020-12-06
For each polynomial function, one zero is given. Find all rational zeros and factor the polynomial. Then graph the function. f(x)=3x^{3}+x^{2}-10x-8ZSK, zero:2
asked 2021-02-20
Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. \(\displaystyle{y}={x}^{{{3}}}-{3}{x}^{{{2}}},{\left[-{2},{5}\right]}{b}{y}{\left[-{10},{10}\right]}\)
asked 2020-11-08
Graph each polynomial function. Factor first if the expression is not in factored form. PSKf(x)=x^{3}\ +\ 3x^{2}\ -\ 13x\ -\ 15 PSZ
asked 2021-01-13
Graph each polynomial function. Factor first if the expression is not in factored form.
\(\displaystyle{f{{\left({x}\right)}}}={\left({3}{x}-{1}\right)}{\left({x}+{2}\right)}^{{{2}}}\)
asked 2020-12-03
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. \(\displaystyle{a}{)}{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}^{{{2}}}-{1}}}}\ {b}{)}{g{{\left({x}\right)}}}={\frac{{{x}-{2}}}{{{x}^{{{2}}}+{3}{x}+{2}}}}\ {c}{)}{h}{\left({x}\right)}={\frac{{{x}+{5}}}{{{x}^{{{2}}}-{x}-{12}}}}\)
asked 2020-10-28
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. \(\displaystyle{\left({2},\ {1}\right)},\ {\left({3},\ {1}\right)},\ {\left({4},\ −{3}\right)},\ {\left({5},\ {0}\right)}\).
asked 2020-11-23
Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{4}{x}^{{{3}}}-{5}{x}^{{{2}}}+{14}{x}-{15}\)
asked 2020-10-18
Graph each polynomial function. PSKf(x)=x^{4}\ -\ x^{3}\ -\ 6x^{2}\ +\ 4x\ +\ 8 PSZ
asked 2020-10-21
Solve the polynomial inequality graphically. \(\displaystyle{3}{x}^{{{4}}}-{5}{x}^{{{3}}}-{12}{x}^{{{2}}}+{12}{x}+{16}\)
asked 2021-02-12
Graph each polynomial function. Factor first if the expression is not in factored form. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}\)
...