# Get help with graphs of polynomial functions

Recent questions in Polynomial graphs
Polynomial graphs

### Graph the polynomial function. $$\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{4}}}+{8}{x}$$

Polynomial graphs

### Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={\left({x}-{1}\right)}^{{{4}}}$$

Polynomial graphs

### For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Roots of multiplicity 2 at $$\displaystyle{x}={\frac{{{1}}}{{{2}}}}$$ and roots of multiplicity 1 at x = 6 and x = −2. y-intercept at (0,18)

Polynomial graphs

### Modeling: Draw models to represents $$\frac{3}{4}$$ and $$\displaystyle{2}{\frac{{{3}}}{{{5}}}}$$

Polynomial graphs

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

Polynomial graphs

### Graph the polynomial function. $$\displaystyle{f{{\left({x}\right)}}}=-{x}^{{4}}$$

Polynomial graphs

### Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={\left({x}-{1}\right)}^{{4}}$$

Polynomial graphs

### Find the Taylor polynomial T3(x) for the function f centered at the number a. Graph f and T3 on the same screen. $$f(x)=x+e^{-x}, a=0$$

Polynomial graphs

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

Polynomial graphs

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

Polynomial graphs

### 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 $$\displaystyle{y}={x}^{{{3}}}$$. b) State the domain and range of the transformed function. c) Sketch graphs of the base function and the transformed function on the same set of axes.

Polynomial graphs

### Describe any similarities and differences. Refer to the end behaviour, local maximum and local minimum points, and maximum and minimum points. a) Sketch graphs of $$\displaystyle{y}={\sin{\ }}{x}$$ and $$\displaystyle{y}={\cos{\ }}{x}.$$ b) Compare the graph of a periodic function to the graph of a polynomial function.

Polynomial graphs

### Using calculus, it can be shown that the tangent function can be approximated by the polynomial $$\displaystyle{\tan{\ }}{x}\ \approx\ {x}\ +\ {\frac{{{2}{x}^{{{3}}}}}{{{3}!}}}\ +\ {\frac{{{16}{x}^{{{5}}}}}{{{5}!}}}$$ where x is in radians. Use a graphing utility to graph the tangent function and its polynomial approximation in the same viewing window. How do the graphs.

Polynomial graphs

### Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}{\left({x}-{5}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}$$

Polynomial graphs

### (a) find the Maclaurin polynomial $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ for f(x), (b) complete the following $$\begin{array}{|c|c|}\hline x: & -0.75 & -0.50 & -0.25 & 0 & 0.25 & 0.50 & 0.75 \\ \hline \end{array}$$ for f(x) and $$P_{3}(x)$$ and (c) sketch the graphs of f(x) and $$\displaystyle{P}_{{{3}}}{\left({x}\right)}$$ on the same set of coordinate axes. $$\displaystyle{f{{\left({x}\right)}}}={\arctan{{x}}}$$

Polynomial graphs

### Find the quadratic polynomial $$\displaystyle{g{{\left({x}\right)}}}-{a}{x}^{{{2}}}\ +\ {b}{x}\ +\ {c}\ \text{which best fits the function}\ {f{{\left({x}\right)}}}={e}^{{{x}}}\ \text{at}\ {x}={0},\ \text{in the sense that}\ {g{{\left({0}\right)}}}={f{{\left({0}\right)}}},\ \text{and}\ {g}'{\left({0}\right)}={f}'{\left({0}\right)},\ \text{and}\ {g}{''}{\left({0}\right)}={f}{''}{\left({0}\right)}.$$ Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?

Polynomial graphs

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

Polynomial graphs

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

Polynomial graphs