Recent questions in Polynomial graphs

Polynomial graphs

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asked 2021-03-18

Sketch graphs of each of the following polynomial functions. Be sure to label the x- and they-intercepts of each graph. \(\displaystyle{a}.{y}={x}{\left({2}{x}+{3}\right)}{\left({2}{x}-{5}\right)}{b}.{y}={\left({11}-{2}{x}\right)}^{{{2}}}{\left({x}-{2}\right)}\)

Polynomial graphs

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asked 2021-02-26

a) Identify the parameters a, k, d, and c in the polynomial function \(\displaystyle{y}={\frac{{{1}}}{{{3}}}}{\left[-{2}{\left({x}+{3}\right)}\right]}^{{{4}}}-{1}\). Describe how each parameter transforms the base function \(\displaystyle{y}={x}^{{{4}}}\). b) State the domain and range, the vertex, and the equation of the axis of symmetry of the transformed function. c) Describe two possible orders in which the transformations can be applied to the graph of \(\displaystyle{y}={x}^{{{4}}}\) to produce the graph of \(\displaystyle{y}={\frac{{{1}}}{{{3}}}}{\left[-{2}{\left({x}+{3}\right)}\right]}^{{{4}}}-{1}\). d) Sketch graphs of the base function and the transformed function on the same set of axes.

Polynomial graphs

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asked 2021-02-25

In calculus, it can be shown that the arctangent function can be approximated by the polynomial
\(\displaystyle{\arctan{{x}}}\approx{x}-\frac{{x}^{{{3}}}}{{3}}+\frac{{x}^{{{5}}}}{{5}}-\frac{{x}^{{{7}}}}{{7}}\)
where x is in radians. Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare?

Polynomial graphs

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asked 2021-02-25

Sketch the graphs of two functions that are not polynomial functions.
a) \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
b) \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}}\)
Explain your reasoning.

Polynomial graphs

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asked 2021-02-22

Investigate the change in the graph of a sinusoidal function of the form \(\displaystyle{\quad\text{and}\quad}={\sin{{x}}}{\quad\text{or}\quad}{\quad\text{and}\quad}={\cos{{x}}}\) when multiplied by a polynomial function. Use a graphing calculator to sketch the graphs of and \(\displaystyle={2}{x},{\quad\text{and}\quad}=-{2}{x},{\quad\text{and}\quad}={2}{x}{\cos{{x}}}\) on the same coordinate plane, on the interval \(\displaystyle{\left[-{20},{20}\right]}.\)

Polynomial graphs

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asked 2021-02-20

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{{4}}}+{7}{x}^{{{2}}}-{2}\)

Polynomial graphs

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asked 2021-02-03

Graph each polynomial function. \(f(x)=2x^{3}\ -\ x^{2}\ +\ 2x\ -\ 1\)

Polynomial graphs

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asked 2021-01-28

Solve the polynomial inequality graphically. \(\displaystyle{x}^{{{3}}}-{x}^{{{2}}}-{2}{x}\geq{0}\)

Polynomial graphs

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asked 2021-01-25

Using calculus, it can be shown that the secant function can be approximated by the polynomial \(\displaystyle{\sec{{x}}}\approx{1}+{\frac{{{x}^{{{2}}}}}{{{2}!}}}+{\frac{{{5}{x}^{{{4}}}}}{{{4}!}}}\) where x is in radians. Use a graphing utility to graph the secant function and its polynomial approximation in the same viewing window. How do the graphs compare?

Polynomial graphs

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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. \(\displaystyle{a}{)}{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}^{{{2}}}-{1}}}}\ {b}{)}{g{{\left({x}\right)}}}={\frac{{{x}-{2}}}{{{x}^{{{2}}}+{3}{x}+{2}}}}\ {c}{)}{h}{\left({x}\right)}={\frac{{{x}+{5}}}{{{x}^{{{2}}}-{x}-{12}}}}\)

Polynomial graphs

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asked 2020-12-02

Graph each polynomial function.\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}+{2}{x}^{{{2}}}-{5}{x}-{6}\)

Polynomial graphs

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asked 2020-11-20

Graph each polynomial function. Factor first if the expression is not in factored form.
\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}^{{{2}}}−{4}\right)}{\left({x}−{1}\right)}\)

Polynomial graphs

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asked 2020-11-05

Using calculus, it can be shown that the arctangent function can be approximated by the polynomial
\(\displaystyle{\arctan{\ }}{x}\ \approx\ {x}\ -\ {\frac{{{x}^{{{3}}}}}{{{3}}}}\ +\ {\frac{{{x}^{{{5}}}}}{{{5}}}}\ -\ {\frac{{{x}^{{{7}}}}}{{{7}}}}\)
where x is in radians.
a) Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare?
b) Study the pattern in the polynomial approximation of the arctangent function and predict the next term. Then repeat part (a). How does the accuracy of the approximation change when an additional term is added?

Polynomial graphs

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asked 2020-10-27

Solve the polynomial inequality graphically. \(\displaystyle{2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}{>}{0}\)

Polynomial graphs

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asked 2020-10-18

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Recent questions in Polynomial graphs

Sketch graphs of each of the following polynomial functions. Be sure to label the x- and they-intercepts of each graph. \(\displaystyle{a}.{y}={x}{\left({2}{x}+{3}\right)}{\left({2}{x}-{5}\right)}{b}.{y}={\left({11}-{2}{x}\right)}^{{{2}}}{\left({x}-{2}\right)}\)

Sketch the graphs of two functions that are not polynomial functions.
a) \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
b) \(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}}\)
Explain your reasoning.

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{{4}}}+{7}{x}^{{{2}}}-{2}\)

Graph each polynomial function. \(f(x)=2x^{3}\ -\ x^{2}\ +\ 2x\ -\ 1\)

Solve the polynomial inequality graphically. \(\displaystyle{x}^{{{3}}}-{x}^{{{2}}}-{2}{x}\geq{0}\)

Graph each polynomial function.\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}+{2}{x}^{{{2}}}-{5}{x}-{6}\)

Graph each polynomial function. Factor first if the expression is not in factored form.
\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}^{{{2}}}−{4}\right)}{\left({x}−{1}\right)}\)

Solve the polynomial inequality graphically. \(\displaystyle{2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}{>}{0}\)

Graph each polynomial function. \(f(x)=x^{4}\ -\ x^{3}\ -\ 6x^{2}\ +\ 4x\ +\ 8 \)

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Precalculus: polynomial graphs solutions

Recent questions in Polynomial graphs