Roots of Polynomial Functions: The roots of polynomial equation's are the points at which y=0 for y=f(x)=(x-a)(x-b) where a,b ∈ R.

Question

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.

asked 2021-05-22

Describe the key characteristics of the graphs of rational functions of the form \(\displaystyle{f{{\left({x}\right)}}}=\frac{{{a}{x}+{b}}}{{{c}{x}+{d}}}\). Explain how you can determine these characteristics using the equations of the functions. In what ways are the graphs of all the functions in this family alike? In what ways are they different? Use examples in your comparison.

asked 2021-05-17

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.

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

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

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