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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 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

^Never true

E. A quadratic function will have at most 2 x-intercepts

Always true

F. A quintic function and a cubic function has the same range


  • Pre-Calculus -

    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.

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