# Graph each polynomial function. f(x)=4x^{4}+7x^{2}-2

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

2021-02-21

### Relevant Questions

Graph each polynomial function. PSKf(x)=x^{4}\ -\ x^{3}\ -\ 6x^{2}\ +\ 4x\ +\ 8 PSZ
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.
Graph each polynomial function. Factor first if the expression is not in factored form.
$$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}{\left({x}^{{{2}}}−{4}\right)}{\left({x}−{1}\right)}$$
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. $$\displaystyle{a}{)}{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}^{{{2}}}-{1}}}}\ {b}{)}{g{{\left({x}\right)}}}={\frac{{{x}-{2}}}{{{x}^{{{2}}}+{3}{x}+{2}}}}\ {c}{)}{h}{\left({x}\right)}={\frac{{{x}+{5}}}{{{x}^{{{2}}}-{x}-{12}}}}$$
Graph each polynomial function.$$\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}+{2}{x}^{{{2}}}-{5}{x}-{6}$$
Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{4}{x}^{{{3}}}-{5}{x}^{{{2}}}+{14}{x}-{15}$$
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?
Graph each polynomial function. Factor first if the expression is not in factored form. $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}+{3}\right)}{\left({x}+{2}\right)}^{{{2}}}$$
Sketch graphs of each of the following polynomial functions. Be sure to label the x- and they-intercepts of each graph. $$\displaystyle{a}.{y}={x}{\left({2}{x}+{3}\right)}{\left({2}{x}-{5}\right)}{b}.{y}={\left({11}-{2}{x}\right)}^{{{2}}}{\left({x}-{2}\right)}$$