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GP2-‐PAP-‐S5-‐HW2-‐Answers
(up, down) As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞ Note; The polynomial function has an odd degree and a negative leading coefficient.
(up, up) As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → ∞, 𝑥 → ∞ Note; The polynomial function has an even degree and a positive leading coefficient.
(down, down) As 𝑦 → −∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞ Note; The polynomial function has an even degree and a negative leading coefficient.
(down, up) As 𝑦 → −∞, 𝑥 → −∞ and as 𝑦 → ∞, 𝑥 → ∞ Note; The polynomial function has an odd degree and a positive leading coefficient.
The polynomial function is not written in standard form. The leading coefficient is !!
! and the degree is 3. The end
behavior is (up, down); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is not written in standard form. The leading coefficient is −1 and the degree is 2. The end behavior is (down, down); As 𝑦 → −∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is written in standard form. The leading coefficient is 1 and the degree is 4. The end behavior is (up, up); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → ∞, 𝑥 → ∞
The polynomial function is not written in standard form. The leading coefficient is !!
! and
the degree is 5. The end behavior is (up, down); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is not written in standard form. The leading coefficient is −1 and the degree is 1. The end behavior is (up, down); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is not written in standard form. The leading coefficient is −1 and the degree is 3. The end behavior is (up, down); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is not written in standard form. The leading coefficient is −3 and the degree is 3. The end behavior is (up, down); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → −∞, 𝑥 → ∞
The polynomial function is written in standard form. The leading coefficient is 1 and the degree is 4. The end behavior is (up, up); As 𝑦 → ∞, 𝑥 → −∞ and as 𝑦 → ∞, 𝑥 → ∞
To find the y-‐intercept, let x = 0 𝑓 0 = 0, so the 𝑦-‐intercept is 𝑦 = 0 To find the x-‐intercept(s), let y = 0 0 = 𝑥! 𝑥 − 1 ! 3𝑥 − 4 Zeros (x-‐intercepts)
Multiplicity Cross or Touch-‐n-‐turn
𝑥 = 0 3 cross 𝑥 = 1 2 Touch-‐n-‐turn
𝑥 =43
1 cross
𝑓 𝑥 = 𝑥 − 2 ! 𝑥 + 2 ! 𝑥 + 2 𝑥 − 2
𝑓 𝑥 = 𝑥 − 2 ! 𝑥 + 2 !
To find the y-‐intercept, let x = 0 𝑓 0 = 0− 2 ! 0+ 2 ! 0! − 4 = −256 To find the x-‐intercept(s), let y = 0 Zeros (x-‐intercepts)
Multiplicity Cross or Touch-‐n-‐turn
𝑥 = 2 5 cross 𝑥 = −2 3 cross
𝑓 𝑥 = 𝑥 − 6 𝑥 + 2 𝑥 + 2 𝑥 + 5 𝑓 𝑥 = 𝑥 + 2 ! 𝑥 − 6 𝑥 + 5
To find the y-‐intercept, let x = 0 𝑓 0 = −12 10 = −120 To find the x-‐intercept(s), let y = 0 Zeros (x-‐intercepts)
Multiplicity Cross or Touch-‐n-‐turn
𝑥 = −2 2 Touch-‐n-‐turn 𝑥 = 6 1 cross 𝑥 = −5 1 cross
𝑓 𝑥 = 𝑥! + 9 𝑥! − 9
𝑓 𝑥 = 𝑥! + 9 𝑥 + 3 𝑥 − 3
To find the y-‐intercept, let x = 0 𝑓 0 = 81 To find the x-‐intercept(s), let y = 0 Zeros (x-‐intercepts)
Multiplicity Cross or Touch-‐n-‐turn
𝑥 = −3 1 cross 𝑥 = 3 1 cross
𝑓 𝑥 = 7𝑥! 3𝑥 − 5 3𝑥 + 7 2𝑥 3𝑥! + 𝑥 − 10
𝑓 𝑥 = 14𝑥! 3𝑥 − 5 3𝑥 + 7 3𝑥 − 5 𝑥 + 2
𝑓 𝑥 = 14𝑥! 3𝑥 − 5 ! 3𝑥 + 7 𝑥 + 2
To find the y-‐intercept, let x = 0 𝑓 0 = 0 To find the x-‐intercept(s), let y = 0 Zeros (x-‐intercepts)
Multiplicity Cross or Touch-‐n-‐turn
𝑥 = 0 4 Touch-‐n-‐turn
𝑥 =53
2 Touch-‐n-‐turn
𝑥 =−73
1 cross
𝑥 = −2 1 cross