4.a Graphs of Polynomial Functions

A 5th degree polynomial has a positive leading coefficient. Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

A linear polynomial has a negative leading coefficient. Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

A 4th degree polynomial has a negative leading coefficient. Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

A quadratic polynomial has a positive leading coefficient. Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

Given the equation: y = -2x³ + 3x + 1

Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

Given the equation: f(x) = 4x - 2 + 5x⁷

Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

Given the equation: f(x) = 1 + 2x⁶ + x² - 2x⁶

Identify the following:

1

Maximum number of relative maxima/minima.

1

Maximum number of x-intercepts.

1

End behavior of the polynomial.

As x → -∞, f(x) → ∞

As x → -∞, f(x) → -∞

As x → ∞, f(x) → ∞

As x → ∞, f(x) → -∞

1

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

1

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

1

What is the minimum degree of the polynomial?

1

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

1

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

1

What is the minimum degree of the polynomial?

1

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

1

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

1

4.a Graphs of Polynomial Functions

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

What is the minimum degree of the polynomial?

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

What is the minimum degree of the polynomial?

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

What is the minimum degree of the polynomial?

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

Maximum number of relative maxima/minima.

Maximum number of x-intercepts.

End behavior of the polynomial.

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

End behavior of the polynomial.

What is the minimum degree of the polynomial?

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

End behavior of the polynomial.

What is the minimum degree of the polynomial?

What are the interval(s) where the function is increasing? Write your answers as with no spaces and reading left to right.

What are the interval(s) where the function is decreasing? Write your answers as with no spaces and reading left to right.

End behavior of the polynomial.

What is the minimum degree of the polynomial?

End behavior of the polynomial.

End behavior of the polynomial.

End behavior of the polynomial.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is increasing?
Write your answers as
with no spaces and reading left to right.

What are the interval(s) where the function is decreasing?
Write your answers as
with no spaces and reading left to right.