Characteristics of the Graphs of Polynomials

How would you describe the point at (0,6)?

• Local Minimum

• Absolute Minimum

• Local Maximum

• Absolute Maximum

Check all the intervals where this graph is increasing.

• (-∞, -1)

• (-1, 0)

• (0, 1)

• (1, ∞)

What is the Domain of the function being graphed?

• (-∞, ∞)

• [7, ∞)

• (-∞, 7]

• (-1, 1)

• (-∞, 7)

Which statements describe the End Behavior of the graph?

• x→ -∞, f(x)→ -∞

• x→ -∞, f(x)→∞

• x→ ∞, f(x)→∞

• x→ ∞, f(x)→ -∞

Which characteristics are correct for the graph?

• a < 0

  3 distinct real zeros

  1 zero with multiplicity 2

• a > 0

  3 distinct real zeros

  1 zero with multiplicity 2

• a > 0

  3 distinct real zeros

  no zeros with multiplicity 2

• a < 0

  3 distinct real zeros

  no zeros with multiplicity 2

Payton was asked to sketch a graph of a function that met the following criteria:

I. The leading coefficient is negative.

II. (x+3) is a factor of f(x).

III. f(x) has an odd degree.

IV. f(x) has an x-intercept at x=5

with multiplicity 3.

• III only

• II and III only

• III and IV only

• I, II, III, and IV

Describe the polynomial. Choose two correct answers.

• Positive 

• Negative

• Odd 

• Even

Select ALL the statements that are true.

• Each x-intercept has an odd multiplicity.

• The numeric degree is 6.

• There is not an absolute maximum but there are two relative maximums.

• The degree is even and the leading coefficient is positive.

Match the graph to the function

• f(x) = x⁵-1

• f(x) = x⁵-6x³+8x+1

• f(x) = x³+8x+1

• f(x) = -x⁵-6x³+8x+1

Describe the polynomial. Choose two correct answers.

• Positive 

• Negative

• Odd 

• Even