Daphne Broadhurst

Answered 2021-08-03
Author has **5730** answers

asked 2021-09-19

asked 2021-06-27

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 \(\displaystyle{\left[-{20},{20}\right]}.\)

asked 2021-05-31

How can proficiency in factoring help when graphing polynomial functions without using a calculator?

asked 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.

\(\displaystyle{a}{)}{f{{\left({x}\right)}}}={\frac{{{x}}}{{{x}^{{{2}}}-{1}}}}\ \)

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

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

asked 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) \(\displaystyle{a}.{f{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}{x}^{{{2}}}+{2}{x}\ {b}.{f{{\left({x}\right)}}}={x}{\left({x}+{1}\right)}^{{{2}}}{\left({x}-{1}\right)}^{{{2}}}\ {c}.{f{{\left({x}\right)}}}={x}^{{{3}}}-{x}^{{{2}}}+{31}{x}+{40}\)

asked 2021-06-13

Carla is using the Rational Root Theorem and synthetic division to find real roots of polynomial functions and sketch their graphs. She says she has wasted her time when she tests a possible root and finds a nonzero remainder instead. Do you agree with her statement? Explain your reasoning.