Pre-Calculus

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geometry

    Is it always true, sometimes true, or never true that the circumcenter is outside its associated triangle?
  2. basic math

    Is it always true, sometimes true, or never true that a regular quadrilateral has two or more obtuse exterior angles?
  3. math

    Determine whether the statement is always true, sometimes true, or never true. 3) The length of the hypotenuse of a right triangle equals the length of one of the legs of the triangle. Answer choice: a.) always true b.) sometimes true …
  4. geometry

    Is it always true, sometimes true, or never true that the centroid is outside its associated triangle?
  5. Math

    a.)If ABCD is a parallelogram, then ABCD is (always true, sometimes true, OR never true) a rectangle. b.)The diagonals of a square (always true, sometimes true, OR never true) bisect each other. c.)If WXYZ is a rectangle, then the …
  6. algebra

    If you have a^ + b^= (a+b)(a+b). Is this always true, never true, or sometimes true?
  7. Math

    if a polynomial function is of degree n, then the graph will have n-1 relative maximum and minimum points. Is this: Always True, Sometimes True, or Never True?
  8. Calculus theory

    Determine if the statement is always true, sometimes true, or never true. If y is a function of x, and is also a function of t. then dy/dx = dy/dt explain. i think its sometimes true but i don't know why it is. am i right?
  9. Math

    Decide whether each statement is always true, sometimes true, or never true.
  10. Math

    Decide whether the given statement is always, sometimes, or never true. The domain of a rational expression and any simplified form are equivalent. a. sometimes true b. never true c. always true

More Similar Questions