Is this graph a function? Explain why or why not.
2 answers:
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Answer: right side behavior:
f(x) is Decreasing
g(x) is Increasing
h(x) is Increasing
j(x) is Decreasing
<u>Step-by-step explanation:</u>
The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial
<u>Sign of leading coefficient</u> (term with greatest exponent):
- If sign is positive, then right side is increasing
- If sign is negative, then right side is decreasing
<u>Degree of polynomial</u> (greatest exponent of polynomial:
- If even, then end behavior is the same from the left and right
- If odd, then end behavior is opposite from the left and right
f(x) = -2x²
- Sign is negative so right side is decreasing
- Degree is even so left side is the same as the right side (decreasing)
as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Decreasing
g(x) = (x + 2)³
- Sign is positive so right side is increasing
- Degree is odd so left side is opposite of the right side (decreasing)
as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -∞ Decreasing
- Sign is positive so right side is increasing
- Degree is an even <u>fraction</u> so left side is opposite of the right side as it approaches the y-intercept (-1)
as x → +∞, f(x) → +∞ Increasing
as x → -∞, f(x) → -1 Decreasing to -1
- Sign is negative so right side is decreasing
- Degree is odd so left side is opposite of the right side (increasing)
as x → +∞, f(x) → +∞ Decreasing
as x → -∞, f(x) → -∞ Increasing