Maxima and Minima / end Behavior Review

Maxima and Minima

Minimums occur at low points on an interval of a graph.

Minimums occur at high points on an interval of a graph

Relative minimums and maximums occur at turning points.

The Absolute Maximum occurs at the highest point on the graph

The Absolute Minimum occurs at the lowest point on the graph.​

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Multiple Choice

the absolute minimum is located at

• (-2, 3)

• (-1, 0)

• (1, 4)

• (2, -2.5)

Multiple Choice

the point (-1, 0) is an ...

• Absolute Maximum

• Absolute Minimum

• relative Maximum

• relative Minimum

Multiple Choice

the point (1,4) is an .......

• Absolute Maximum

• absolute and local maximum

• Local Maximum

• Local Minimum

Multiple Choice

Identify the relative minimum(s) of this graph?

• (-1,-3)

• (4, -1)

• (-1, -3) and ( 4, -1)

• (-3,2) and (2, 1)

Multiple Choice

Identify the relative maximums of this graph?

• (-3,2)

• (-3,2) and (2, 1)

• (2,1)

• (-1, -3) and (4, -1)

Multiple Choice

Where do you find relative minimums and relative maximums?

• zeros
• y-intercepts
• turning points
• by degree

Multiple Choice

What is the absolute max?

• (0, 36)
• (−2.55, −6.55), (2.55, −6.55)
• (−∞, ∞)
• None

Multiple Choice

What is the absolute minimum value (y-value only)?

• -5

• -3

• 0

• -1

Multiple Choice

In the graph (-2,-5) is....

• an absolute minimum

• both a relative and an absolute minimum

• a relative minimum

• a maximum

Multiple Choice

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Multiple Choice

What is the end behavior of the function

•  x →∞, y→∞ and x→∞, y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
•  x →∞, y→∞ and x→⁻∞, y→0
•  x →∞,y→∞and x→⁻∞, y→⁻∞

Multiple Choice

What is the End behavior on the left side

• x →-∞, y→∞
• x →-∞, y→-∞
• x →∞, y→∞
• x →∞, y→∞

Multiple Choice

Describe the end behavior of the graph.

• x → ∞, y→ ∞ and
  x→ ∞, y→⁻∞
• x → ∞, y→ ∞ and
  x→⁻∞, y→∞
• None of these
• x →∞,y→⁻∞ and
  x→∞, y→⁻∞

Multiple Choice

What is the end behavior on the left side

• x →∞, y→∞
• x →-∞, y→-∞
• x →-∞, y→∞
• x →∞, y→∞

Multiple Choice

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Multiple Choice

Which function has this end behavior?

• -1x⁴-3x³+3
• -2x⁷+2x⁴+4
• 3x⁸+3x⁵-4x+7
• 4x⁵-4x⁴+2x³-9

Multiple Choice

The end behavior of the Polynomial f(x) = -3x⁵ + 2x - 1 is: