300670
Description
Mind Map by maggie.martin11, updated more than 1 year ago
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Created by maggie.martin11
almost 11 years ago
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How to Determine the End
Behaviour of a Polynomial Function
- ODD NUMBER: This means the function
is an Odd-Degree Polynomial (ex. 2x + 3x + 4x +5)
- Is the leading coefficient (leading term) a positive
or negative number?
- Positive [a > 0]
- End Behaviour:
as x→ -∞, y→ -∞
as x→ ∞, y→ ∞
- Example:
- Domain= {x
Range= {y
- Max/Min: Neither positive or negative have a
maximum or minimum
value
- Turning Points: Even number
(The largest number of turning
points is n-1, if n= degree)
- Turning Points: Even number
(The largest number of turning
points is n-1, if n= degree)
- Max/Min: Neither positive or negative have a
maximum or minimum
value
- Domain= {x
Range= {y
- The function starts in the
3rd quadrant and ends in the
1st quadrant
- Example:
- End Behaviour:
as x→ -∞, y→ -∞
as x→ ∞, y→ ∞
- Negative [a < 0]
- End Behaviour:
as x→ -∞, y→ ∞
as x→ ∞, y→ -∞
- Example:
- Domain= {x
Range= {y
- Domain= {x
Range= {y
- The function starts in the 2nd
quadrant and ends in the 4th
quadrant
- Example:
- End Behaviour:
as x→ -∞, y→ ∞
as x→ ∞, y→ -∞
- Positive [a > 0]
- Is the leading coefficient (leading term) a positive
or negative number?
- EVEN NUMBER: This means the function is an
Even-Degree Polynomial (ex. 3x + 4x +5)
- Is the leading coefficient (leading term) a positive
or negative number?
- Positive [a > 0]
- End Behaviour:
as x→ -∞, y→ ∞
as x→ ∞, y→ ∞
- Example:
- Domain= {x
Range= {y|y > a}
- Max/Min: Minimum value→a
- Max/Min: Minimum value→a
- Domain= {x
Range= {y|y > a}
- The function starts in the
2nd quadrant and ends in
the 1st quadrant
- Example:
- End Behaviour:
as x→ -∞, y→ ∞
as x→ ∞, y→ ∞
- Negative [a < 0]
- End Behaviour:
as x→ -∞, y→ -∞
as x→ ∞, y→ -∞
- Example:
- Domain= {x
Range= {y|y < a}
- Max/Min: Maximum value→a
- Turning Points: Odd number
(The largest number of turning
points is n-1, if n= degree)
- Turning Points: Odd number
(The largest number of turning
points is n-1, if n= degree)
- Max/Min: Maximum value→a
- Domain= {x
Range= {y|y < a}
- The function starts in the
3rd quadrant and ends in
the 4th quadrant
- Example:
- End Behaviour:
as x→ -∞, y→ -∞
as x→ ∞, y→ -∞
- Positive [a > 0]
- Is the leading coefficient (leading term) a positive
or negative number?
- Is the largest degree of the Polynomial function an Odd or Even number?
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