Function Extrema

Linearity, Extrema, and End Behavior

Recap on the last few days!

Multiple Choice

Is it linear?

4x - 2y = -1

• yes, it can be written as y=2x+½

• no, x and y are multiplied together

• no, one of the variables appears in the denominator, with an exponent, or under a radical.

Multiple Choice

Is it linear?

x² + x + 3 = 8

• yes, it can be written y=x²+x-5

• no, x and y are multiplied together

• no, one of the variables appears in the denominator, with an exponent, or under a radical.

Multiple Choice

Is it linear?

3xy + 8 = 4y

• yes, it can be written as y=¾ xy+2

• no, x and y are multiplied together.

• no, one of the variables appears in the denominator, with an exponent, or under a radical.

Multiple Choice

Does the graph represent a linear function, a non-linear function, or is it not a function?

• Linear Function

• Non-Linear Function

• Not a Function

Extrema

• Maximums

• Minimums

• Relative Maximums

• Relative Minimums

Multiple Choice

How many extrema are there in this graph?

• 2 relative max, 2 relative min

• 3 relative max, 2 relative min

• 2 relative max, 3 relative min

Multiple Choice

What are the extrema of the graph?

• Relative Max = (2, -3), (1, 2)

  Relative Min = (-3, -1), (-1, 4)

• Relative Max = (-3, -1), (-1, 4)

  Relative Min = (2, -3), (1, 2)

• Relative Max = (-1, -3), (4, -1)

  Relative Min = (-3, 2), (2, 1)

• Relative Max = (-3, 2), (2, 1)

  Relative Min = (-1, -3), (4, -1)

Multiple Choice

What are the extrema of the graph?

• Abs. Max = (0,-4)

  Relative Min = (-1.5,0) and (1.5, 0)

• Relative Max = (0,1.5) and (0, -1.5)

  Abs. Min = (-4,0)

• Abs. Max = (-1.5,0) and (1.5, 0)

  Relative Min = (0,-4)

• Relative Max = (-4,0)

  Relative Min =(0,1.5) and (0, -1.5)

Multiple Choice

What is the location of the absolute maximum for the graphed function?

• 1

• 3

• 4

• 5

• Does Not Exist

End Behavior

•  $x\rightarrow\infty,\ f\left(x\right)\rightarrow?$  
  

   $x\rightarrow-\infty,\ f\left(x\right)\rightarrow?$ 

• Where does the right side of the graph go? Where does the left side of the graph go?

Multiple Choice

Describe the end behavior of the graph.

• x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

• x → -∞, f(x) → ∞ and x→∞, f(x) →∞

• x → -∞, f(x) → ∞ and x→∞, f(x) → 0

• x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

Multiple Choice

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

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

Multiple Choice

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

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