Real-World Polynomial Graphs: Expert Examples and Samples

Suppose f has period 2 and f(x) = x for $0 \leq x < 2$ . Find the fourth-degree Fourier polynomial and graph it on $0 \leq x < 2$

mattgondek4 2021-08-08

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

vazelinahS 2021-08-08

Graph the polynomial $P (x) = - {(x + 2)}^{3} + 27$ , showing clearly all x- and y- intercepts.

Anonym 2021-08-07

Use a graphing calculator to examine the graphs of the following functions. Determine ⋅⋅ the degree of the polynomial ⋅⋅ the leading coefficient ⋅⋅ the end behavior of the polynomial function ⋅⋅ the maximum number of zeros ⋅⋅ the maximum number of turning points (relative maxima and minima) $a . f (x) = \frac{1}{2} x^{2} + 2 x b . f (x) = x {(x + 1)}^{2} {(x - 1)}^{2} c . f (x) = x^{3} - x^{2} + 31 x + 40$

kuCAu 2021-08-06

Graph the polynomial function.
$f (x) = x^{5} + x^{2} - 4$

Ernstfalld 2021-03-18

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

Sinead Mcgee 2021-02-26

a) Identify the parameters a, k, d, and c in the polynomial function $y = \frac{1}{3} {[- 2 (x + 3)]}^{4} - 1$ . Describe how each parameter transforms the base function $y = x^{4}$ . 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 $y = x^{4}$ to produce the graph of $y = \frac{1}{3} {[- 2 (x + 3)]}^{4} - 1$ . d) Sketch graphs of the base function and the transformed function on the same set of axes.

tinfoQ 2021-02-25

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

coexpennan 2021-02-25

In calculus, it can be shown that the arctangent function can be approximated by the polynomial
$\arctan x \approx x - \frac{x^{3}}{3} + \frac{x^{5}}{5} - \frac{x^{7}}{7}$
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?

e1s2kat26 2021-02-22

Investigate the change in the graph of a sinusoidal function of the form $and = \sin x or and = \cos x$ when multiplied by a polynomial function. Use a graphing calculator to sketch the graphs of and $= 2 x, and = - 2 x, and = 2 x \cos x$ on the same coordinate plane, on the interval $[- 20, 20] .$

Nannie Mack 2021-02-20

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

ka1leE 2021-02-03

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

ossidianaZ 2021-01-28

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

Yasmin 2021-01-25

Using calculus, it can be shown that the secant function can be approximated by the polynomial $\sec x \approx 1 + \frac{x^{2}}{2!} + \frac{5 x^{4}}{4!}$ 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?

Bevan Mcdonald 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.

$a) f (x) = \frac{x}{x^{2} - 1}$

$b) g (x) = \frac{x - 2}{x^{2} + 3 x + 2}$

$c) h (x) = \frac{x + 5}{x^{2} - x - 12}$

pedzenekO 2020-12-02

Graph each polynomial function. $f (x) = x^{3} + 2 x^{2} - 5 x - 6$

Brittney Lord 2020-11-20

Graph each polynomial function. Factor first if the expression is not in factored form.
$f (x) = 2 x^{3} (x^{2} - 4) (x - 1)$

tinfoQ 2020-11-05

Using calculus, it can be shown that the arctangent function can be approximated by the polynomial
$\arctan x \approx x - \frac{x^{3}}{3} + \frac{x^{5}}{5} - \frac{x^{7}}{7}$
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?

shadsiei 2020-10-27

Solve the polynomial inequality graphically. $2 x^{3} - 5 x^{2} - x + 6 > 0$

Anish Buchanan 2020-10-18

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

As you are looking for examples of polynomial graphs, take a closer look at various answers as these will help you understand the methods that have been approached. These may include verbal or word explanations and the graphical portrayal of polynomial problems. It is one of the reasons why samples of polynomial graphs must contain analysis. Remember that the answers should contain graphs with values that are invariant, thus meaning that one must refer to the adjacency matrix that comes along. See the provided solutions to learn how it is done.

Precalculus

Polynomial Graphs: Examples and Samples