Extrema and Polynomial Intervals of Increase and Decrease

Pick all statements that apply to this polynomial.

• It is an odd degree function.

• It is an even degree function.

• It has a positive leading coefficient.

• It has a negative leading coefficient.

• It has 3 real roots.

Answer explanation

The polynomial is an odd degree function, indicated by its leading term's degree. It has a negative leading coefficient, which affects its end behavior. Additionally, it has 3 real roots, confirming it crosses the x-axis three times.

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

Using the given table, determine the consecutive integer values of x between which each real zero of the function is located.

Tags

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

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

How would you describe the behavior of this function on the domain interval (-1, 1)?

• increasing

• decreasing

• constant

Does this function have an absolute maximum?

• Yes 

• No

Is interval 3 increasing, decreasing, or constant?

• Increasing

• Decreasing

• Constant

Is interval 4 increasing, decreasing, or constant?

• Increasing

• Decreasing

• Constant

Where is the function decreasing?

• x<−2.5 and 2.5<x<0

• x<-2.5 and x>0 and x>2.5

• x<−2.5 and 0<x<2.5

• x>-2.5 and 0<x>2.5

What is/are the decreasing interval(s) for the function shown?

What is the interval of increase of this function?

• (1, ∞)

• None

• (2, ∞)

• (-∞, ∞)