Characteristics of Polynomials

Characteristics of Polynomials

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​We identify the extrema using x-values!

Multiple Choice

We do: Identify the local minimum

• x = 8

• x = 4

• $$\infty$$

• x = 2

Multiple Choice

We do: What is the location of the absolute maximum for the graphed function?

• x = 1

• x = 3

• x = 4

• x = 5

• Does Not Exist

Multiple Choice

You do: How many extrema (turning points) 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

Multiple Choice

You do: Find the local maximum and minimum

• Local max at x = -3

  Local min at x = -3

• Local max at x = 1

  Local min at x = -3

• Local max at x = -3

  Local min at x = 1

• $$\left(-\infty,\ \infty\right)$$

Multiple Choice

We do: What is the y-intercept of the line 5x-2y=10?

• 0

• 2

• 5

• -2

• -5

Multiple Choice

You do: What is the x-intercept of the line 5x-2y=10?

• 0

• 2

• 5

• -2

• -5

Multiple Choice

We do: Identify where the function is decreasing.

• x < -5 , x > -1

• -5 < x < 1 , x > 8

• x < -5 , -1 < x < 8

• All Real Numbers

Multiple Choice

You do: When is this function increasing?

• −2.5 < x < 2.5

• 0 < x < 5

• 0 < x < 55

• −5 < x < 0

Multiple Choice

We do:

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

We do:

In the above graph complete the following end behavior:

As x --> -∞, f(x) --> ____

As x --> +∞, f(x) --> ____

• -∞

  -∞

• +∞

  -∞

• -∞

  +∞

• +∞

  +∞

Multiple Choice

You do:

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

We do:

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

Multiple Choice

We do:

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

Multiple Choice

You do:

Which root has even multiplicity?

• 1

• -4

• -1

• 2

Multiple Choice

You do:

What is the multiplicity of the zero x=1 for the function  $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$  ?

• 2

• 1

• 4

• 3