Polynomial Graphs: Examples and Explanations

High School
Algebra
Algebra I
Polynomial graphs

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

iohanetc 2021-06-05

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

Chardonnay Felix 2021-06-01

Graph each polynomial function.
$f (x) = {(x - 1)}^{4}$

BolkowN 2021-05-11

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

Tabansi 2021-05-02

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

ddaeeric 2021-02-25

a) Identify the parameters a, b, h, and k in the polynomial $y = \frac{1}{3} {(x + 3)}^{3} - 2$ Describe how each parameter transforms the base function $y = x^{3}$ .
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.

Isa Trevino 2021-02-20

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 $y = \sin x$ and $y = \cos x .$
b) Compare the graph of a periodic function to the graph of a polynomial function.

cistG 2021-02-15

Using calculus, it can be shown that the tangent function can be approximated by the polynomial $\tan x \approx x + \frac{2 x^{3}}{3!} + \frac{16 x^{5}}{5!}$ 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.

sjeikdom0 2021-02-12

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

Dottie Parra 2021-02-02

(a) find the Maclaurin polynomial $P_{3} (x)$ for f(x), (b) complete the following

$\begin{array}{cc} x : & - 0.75 & - 0.50 & - 0.25 & 0 & 0.25 & 0.50 & 0.75 \end{array}$

for f(x) and $P_{3} (x)$ and (c) sketch the graphs of f(x) and $P_{3} (x)$ on the same set of coordinate axes. $f (x) = \arctan x$

aflacatn 2021-01-30

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

Maiclubk 2021-01-22

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

Nannie Mack 2021-01-10

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

usagirl007A 2020-12-30

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

Chaya Galloway 2020-11-23

Graph each polynomial function. $f (x) = x^{4} - 4 x^{3} - 5 x^{2} + 14 x - 15$

Tobias Ali 2020-11-08

Graph each polynomial function. Factor first if the expression is not in factored form. $f (x) = x^{3} + 3 x^{2} - 13 x - 15$

arenceabigns 2020-11-01

For the following exercise, for each polynomial $f (x) = \frac{1}{2} x^{2} - 1$ : a) find the degree, b) find the zeros, if any, c) find the y-intercept(s), if any, d) use the leading coefficient to determine the graph’s end behavior, e) determine algebraically whether the polynomial is even, odd, or neither.

Algebra is never easy when you do not know how to calculate or how to apply various graphs of polynomial functions. These are used in the calculation of the determination of the objects and the engineering tasks. See some polynomial graphs examples with the graphic explanations as some of the answers will have word problems. When you have good explanations, your calculations will be more confident. It is better to look at several answers that will be different in length. If you compare things in the solutions, you will see how to approach polynomial graphs by working with various axes.

Algebra I

Polynomial Equations and Graphs - Answered