PreCalculus
posted by Shreya on .
Graphing Polynomials
Decide whether each of the following is sometimes true, always true, or never true and explain reasoning.
A. A cubic function has 2 different xintercepts
^Never true, has to have 3?
B. A cubic function has 3 xintercepts
^ Always true
C. A quartic function has the range of all real numbers
^ ?
D. A quartic function has no xintercepts
^Never true
E. A quadratic function will have at most 2 xintercepts
Always true
F. A quintic function and a cubic function has the same range
?

A. sometimes true: x(x1)^2
B. Sometimes true x^3 ; x(x1)(x2)
C. never. It always opens up or down.
D. sometimes true. x^4+1
E. always true
F. true. Always has range of all reals.
Every cubic looks like x^3, and every quintic looks like x^5, with some wiggles around the roots, but in the end they all go from infinity to infinity.