Algebra III Graphing Polynomials Review with end behavior

Degree: even
Leading coefficient: negative

as x -?
f(x) -?
as x +?
f(x) -?
As the x values get infinitely negative and positive, the y values get infinitely negative

Degree: even
Leading coefficient: positive

as x -?
f(x) +?
as x +?
f(x) +?
As the x values get infinitely negative and positive, the y values get infinitely positive

Degree: odd
Leading coefficient: negative

as x -?
f(x) +?
as x +?
f(x) -?
As the x values get infinitely negative, the y values get infinitely positive
As the x values get infinitely positive, they values get infinitely negative

Degree: odd
Leading coefficient: positive

as x +?
f(x) +?
as x -?
f(x) -?
As the x values get infinitely negative, the y values get infinitely negative
AS the x values get infinitely positive, the y values get infinitely positive

2

# of relative maximum points?

6

# of real zeros?

3

# of relative minimum points?

1

# of relative maximum points?

3

# of real zeros?

2

# real zeros?

4

# real zeros?

0

# real zeros?

1

# of real zeros?

3

# real zeros?

No

Is there a relative maximum at x = 0?

Yes

Is there a relative minimum at x = 0?

Odd

Odd or even?

Leading Coefficient: -
Degree: Even
# of Real Roots: 0
# of Complex Roots: 4

Leading Coefficient: -
Degree: Even
# of Real Roots: 4
# of Complex Roots: 0

Leading Coefficient: +
Degree: Odd
# of Real Roots: 1
# of Complex Roots: 2

Leading Coefficient: +
Degree: Even
# of Real Roots: 2
# of Complex Roots: 2

Leading Coefficient: -
Degree: Odd
# of Real Roots: 1
# of Complex Roots: 2

Leading Coefficient: -
Degree: Odd
# of Real Roots: 3
# of Complex Roots: 0

Leading Coefficient: -
Degree: 5
Roots: -4,-1,0,5

Leading Coefficient: -
Degree: 6
Roots: -2,-1,5,6

Leading Coefficient: +
Degree: 6
Roots: -6,-3,1

Leading Coefficient: +
Degree: 7
Roots: -6,-3,1,2

Leading Coefficient: +
Degree: 8
Roots: -4,-1,2,4

Leading Coefficient: +
Degree: 7
Roots: -6,-3,2,6

Degree: even
Leading coefficient: negative

as x -?
f(x) -?
as x +?
f(x) -?
As the x values get infinitely negative and positive, the y values get infinitely negative

Degree: even
Leading coefficient: positive

as x -?
f(x) +?
as x +?
f(x) +?
As the x values get infinitely negative and positive, the y values get infinitely positive

Degree: odd
Leading coefficient: negative

as x -?
f(x) +?
as x +?
f(x) -?
As the x values get infinitely negative, the y values get infinitely positive
As the x values get infinitely positive, they values get infinitely negative

Degree: odd
Leading coefficient: positive

as x +?
f(x) +?
as x -?
f(x) -?
As the x values get infinitely negative, the y values get infinitely negative
AS the x values get infinitely positive, the y values get infinitely positive

2

# of relative maximum points?

6

# of real zeros?

3

# of relative minimum points?

1

# of relative maximum points?

3

# of real zeros?

2

# real zeros?

4

# real zeros?

0

# real zeros?

1

# of real zeros?

3

# real zeros?

No

Is there a relative maximum at x = 0?

Yes

Is there a relative minimum at x = 0?

Odd

Odd or even?

Leading Coefficient: -
Degree: Even
# of Real Roots: 0
# of Complex Roots: 4

Leading Coefficient: -
Degree: Even
# of Real Roots: 4
# of Complex Roots: 0

Leading Coefficient: +
Degree: Odd
# of Real Roots: 1
# of Complex Roots: 2

Leading Coefficient: +
Degree: Even
# of Real Roots: 2
# of Complex Roots: 2

Leading Coefficient: -
Degree: Odd
# of Real Roots: 1
# of Complex Roots: 2

Leading Coefficient: -
Degree: Odd
# of Real Roots: 3
# of Complex Roots: 0

Leading Coefficient: -
Degree: 5
Roots: -4,-1,0,5

Leading Coefficient: -
Degree: 6
Roots: -2,-1,5,6

Leading Coefficient: +
Degree: 6
Roots: -6,-3,1

Leading Coefficient: +
Degree: 7
Roots: -6,-3,1,2

Leading Coefficient: +
Degree: 8
Roots: -4,-1,2,4

Leading Coefficient: +
Degree: 7
Roots: -6,-3,2,6