Consider the following four polynomial functions: f(x)=-2x^3, ; g(x)=3x^4, ;…
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the following four polynomial functions:
f(x)=−2x3,g(x)=3x4,h(x)=−x2,k(x)=4x5.
Answer the questions given below without sketching detailed graphs.
(i) Identify which of the above functions will have graphs that are symmetric about the y-axis and which will be symmetric about the origin. Give reasons for each answer.
(ii) For every function, state whether its graph opens upwards, opens downwards, rises from left to right, or falls from left to right. Use the degree and the sign of the leading coefficient to justify your statements.
(iii) Indicate, for each function, whether the graph possesses a global minimum, a global maximum or neither.