High school polynomial graphs problems, solved and explained

Solve the polynomial inequality graphically.
\(\displaystyle−{x}^{{3}}−{3}{x}^{{2}}−{9}{x}+{4}{<}{0}\)

Polynomial graphs

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asked 2021-09-16

The graph of a polynomial function has the following characteristics: a) Its domain and range are the set of all real numbers. b) There are turning points at x = -2, 0, and 3. a) Draw the graphs of two different polynomial functions that have these three characteristics. b) What additional characteristics would ensure that only one graph could be drawn?

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asked 2021-09-15

If the result of a polynomial division is \(\displaystyle{2}{x}^{{{3}}}−{4}{x}^{{{2}}}−{5}{x}+{23}{x}+{2}\) , make at least three definitive statements

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asked 2021-09-02

Do you agree with the contention that the functions \(f(x) = x + 2\) and \(g(x)=\displaystyle{\frac{{{x}^{{{2}}}-{4}}}{{{x}-{2}}}}\) are the same in every respect. Provide evidence to support your position.

Polynomial graphs

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asked 2021-08-16

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

Polynomial graphs

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asked 2021-08-16

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

Polynomial graphs

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asked 2021-08-13

Graph the polynomial by transforming an appropriate graph of the form \(\displaystyle{y}={x}^{{{n}}}\).
Show clearly all x- and y-intercepts. \(\displaystyle{P}{\left({x}\right)}=-{x}^{{{3}}}+{64}\)

Polynomial graphs

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asked 2021-08-12

Copy and complete the anticipation guide in your notes. StatementThe quadratic formula can only be used when solving a quadratic equation.Cubic equations always have three real roots.The graph of a cubic function always passes through all four quadrants.The graphs of all polynomial functions must pass through at least two quadrants.The expression \(x^2>4\) is only true if x>2.If you know the instantaneous rates of change for a function at x = 2 and x = 3, you can predict fairly well what the function looks like in between.
Agree Disagree Justification
Statement
The quadratic formula can only be used when solving a quadratic equation. Cubic equations always have three real roots. The graph of a cubic function always passes through all four quadrants. The graphs of all polynomial functions must pass through at least two quadrants.
The expression \(x^2>4\) is only true if x>2. If you know the instantaneous rates of change for a function at x = 2 and x = 3, you can predict fairly well what the function looks like in between.

Polynomial graphs

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asked 2021-08-11

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{{5}}}-{8}{x}^{{{4}}}-{x}+{2}\)

Polynomial graphs

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asked 2021-08-11

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}+{3}{x}^{{{2}}}-{4}{x}-{2}\)

Polynomial graphs

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asked 2021-08-08

Graph the polynomial by transforming an appropriate graph of the form \(\displaystyle{y}={x}^{{{n}}}\). Show clearly all x- and y-intercepts.\(\displaystyle{P}{\left({x}\right)}={2}{\left({x}+{1}\right)}^{{{4}}}-{32}\)

Polynomial graphs

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asked 2021-08-06

Graph the polynomial function.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{5}}}+{x}^{{{2}}}-{4}\)

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.

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

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asked 2021-02-03

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

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asked 2021-01-28

Ask your question. Get your answer. Easy as that

Solve the polynomial inequality graphically.
\(\displaystyle−{x}^{{3}}−{3}{x}^{{2}}−{9}{x}+{4}{<}{0}\)

If the result of a polynomial division is \(\displaystyle{2}{x}^{{{3}}}−{4}{x}^{{{2}}}−{5}{x}+{23}{x}+{2}\) , make at least three definitive statements

Do you agree with the contention that the functions \(f(x) = x + 2\) and \(g(x)=\displaystyle{\frac{{{x}^{{{2}}}-{4}}}{{{x}-{2}}}}\) are the same in every respect. Provide evidence to support your position.

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

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

Graph the polynomial by transforming an appropriate graph of the form \(\displaystyle{y}={x}^{{{n}}}\).
Show clearly all x- and y-intercepts. \(\displaystyle{P}{\left({x}\right)}=-{x}^{{{3}}}+{64}\)

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{{5}}}-{8}{x}^{{{4}}}-{x}+{2}\)

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}+{3}{x}^{{{2}}}-{4}{x}-{2}\)

Graph the polynomial by transforming an appropriate graph of the form \(\displaystyle{y}={x}^{{{n}}}\). Show clearly all x- and y-intercepts.\(\displaystyle{P}{\left({x}\right)}={2}{\left({x}+{1}\right)}^{{{4}}}-{32}\)

Graph the polynomial function.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{5}}}+{x}^{{{2}}}-{4}\)

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. \(\displaystyle{x}^{{{3}}}-{x}^{{{2}}}-{2}{x}\geq{0}\)

Ask your question. Get your answer. Easy as that

Polynomial graphs with equation