Domain and Range Relative Maxima/Minima Polynomials

How many extrema are there in this graph?

• 2 max, 2 min

• 3 max, 2 min

• 2 man, 3 min

• 3 increasing intervals, 2 decreasing intervals

• 2 increasing intervals, 3 decreasing intervals

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c

Select all statements that apply to this graphed polynomial...

• The domain

  is (-∞, ∞)

• The range

  is (-∞, ∞)

• The range

  is [-4, ∞)

• There is one absolute minimum

• There are no local maximum

Answer explanation

The domain of a polynomial is always (-∞, ∞). The range is [-4, ∞) indicating a minimum value of -4. There is one absolute minimum at this point, and no local maximum exists in this polynomial.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c

Select all statements that apply to the graphed polynomial...

• The domain

  is (-∞, ∞)

• The range

  is (-∞, ∞)

• The range

  is (-∞, 6)

• There is 1 absolute maximum

• There are 1 local minimum, 1 local maximum

Answer explanation

The domain of a polynomial is always (-∞, ∞). The range is also (-∞, ∞) if it does not have a maximum or minimum. The graph shows 1 local minimum and 1 local maximum, confirming these statements.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c

• 0

• 1

• 4

• -1

• 2

• 5

Answer explanation

To find extrema, we calculate the derivative f'(x) = -6x^2 + 24x - 8 and set it to zero. Solving gives x = 0, 1, and 4. The relative minimum occurs between x = 0 and x = 1, and the relative maximum is at x = 4.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c

What is the relative max of this function?

• x = 5

• infinity

• there is no relative maximum

• 2.5 and it occurs at x = 5

Where is there a relative max?

• x = 3

• x = -1

• x = 1

• x = 0

What is the range?

The domain of a polynomial function is always (-∞, +∞).

• True

• False

What is the domain of a polynomial function?

• It depends on the degree of the function being even or odd.

• [0,∞)

• (-∞,∞)

• It depends on the vertex

The domain of a polynomial function is always (-∞, ∞).

• True

• False