Posted by Shreya on .
Decide whether each of the following is sometimes true, always true, or never true and explain reasoning.
A. A cubic function has 2 different x-intercepts
^Never true, has to have 3?
B. A cubic function has 3 x-intercepts
^ Always true
C. A quartic function has the range of all real numbers
D. A quartic function has no x-intercepts
E. A quadratic function will have at most 2 x-intercepts
F. A quintic function and a cubic function has the same range
A. sometimes true: x(x-1)^2
B. Sometimes true x^3 ; x(x-1)(x-2)
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.