for polynomial function:

Question

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the behavior of the graph near each x-intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x| .

Answer 1

Step 1:

(a)

The polynomial function is .

The definition of real zeros :.

The real zeros of this polynomial function are .

The definition of zeros of multiplicity :, the exponent of factor is .

At the zeros of multiplicity is .

At the zeros of multiplicity is .

Step 2:

(b)

Find x-intercept substitute in function.

The polynomial function is .

The graph crosses or touches the -axis at and .

Solution :

(a)

At the zeros of multiplicity is .

At the zeros of multiplicity is .

(b)

The graph crosses or touches the -axis at and .