University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2021
Views:

255

Pages:

2
Author:

Olive Estrada

Pre-Calculus/Trig UNIT 2: Polynomial Functions – SECTION 1 WORKSHEET ANSWER KEY Directions: Determine the intervals over which the function is increasing, decreasing, or constant. 3 2.) 𝑓(𝑥) = 𝑥 2 − 4𝑥 1.) 𝑓(𝑥) = 2 𝑥 INCREASING 3.) 𝑓(𝑥) = 𝑥 3 − 3𝑥 2 + 2 INCREASING INCREASING 4.) 𝑓(𝑥) = √𝑥 2 − 1 INCREASING (−∞, ∞) (2, ∞) (−∞, 0) ∪ (2, ∞) (1, ∞) DECREASING DECREASING DECREASING DECREASING NONE (−∞, 𝟐) (𝟎, 𝟐) (−∞, −𝟏) CONSTANT CONSTANT CONSTANT CONSTANT NONE NONE NONE NONE 5.) 𝑓(𝑥) = |𝑥 + 1| + |𝑥 − 1| INCREASING DECREASING CONSTANT (𝟏, ∞) (−∞, −𝟏) (−𝟏, 𝟏) 𝑥 + 3, 𝑥 ≤ 0 3, 0 < 𝑥 ≤ 2 8.) 𝑓(𝑥) = { 2𝑥 − 1, 𝑥 > 2 1 6.) 𝑓(𝑥) = 𝑥−2 7.) 𝑓(𝑥) = 𝑥 2 +𝑥+1 𝑥+1 INCREASING NONE INCREASING (−∞, −𝟐) ∪ (𝟎, ∞) DECREASING (−∞, 𝟐) ∪ (𝟐, ∞) DECREASING (−𝟐, −𝟏) ∪ (−𝟏, 𝟎) CONSTANT NONE CONSTANT NONE 9.) 𝑓(𝑥) = { |𝑥 + 3|, 𝑥 < −2 −1, −2 ≤ 𝑥 < 1 √𝑥 − 1, 𝑥 > 1 2𝑥 + 1, 𝑥 ≤ −1 10.) 𝑓(𝑥) = { 2 𝑥 − 2, 𝑥 > −1 INCREASING (−∞, 𝟎) ∪ (𝟐, ∞) INCREASING (−𝟑, −𝟐) ∪ (𝟏, ∞) INCREASING (−∞, −𝟏) ∪ (𝟎, ∞) DECREASING NONE (𝟎, 𝟐) DECREASING (−∞, −𝟑) [−𝟐, 𝟏) DECREASING (−𝟏, 𝟎) NONE CONSTANT CONSTANT CONSTANT Directions: Determine whether the function is even, odd, or neither. Then describe the symmetry. 11.) 𝑓(𝑥) = 𝑥 6 − 2𝑥 2 + 3 12.) 𝑓(𝑥) = 𝑥 3 − 5 EVEN; 𝒚-axis symmetry 13.) 𝑓(𝑥) = 𝑥 3 − 5𝑥 NEITHER ODD; origin symmetry 2 15.) 𝑓(𝑡) = 𝑡 2 + 2𝑡 − 3 14.) 𝑓(𝑥) = 𝑥√1 − 𝑥 2 ODD; origin symmetry 16.) 𝑓(𝑠) = 4𝑠 3 EVEN; 𝒚-axis symmetry NEITHER Directions: Match the polynomial function with its graph. C _____ F D _____ G _____ A _____ B H _____ E _____ 18.) 𝑓(𝑥) = 𝑥 2 − 4𝑥 _____ 17.) 𝑓(𝑥) = −2𝑥 + 3 20.) 𝑓(𝑥) = 2𝑥 3 − 3𝑥 + 1 23.) 𝑓(𝑥) = 𝑥 4 + 2𝑥 3 _____ 19.) 𝑓(𝑥) = −2𝑥 2 − 5𝑥 1 4 21.) 𝑓(𝑥) = − 𝑥 4 + 3𝑥 2 1 1 3 22.) 𝑓(𝑥) = − 𝑥 3 + 𝑥 2 − 4 3 9 24.) 𝑓(𝑥) = 5 𝑥 5 − 2𝑥 3 + 5 𝑥 A B C D E F G H Directions: Describe the right-hand and left-hand end behavior of the graph of the polynomial function. 1 25.) 𝑓(𝑥) = 3 𝑥 3 + 5𝑥 𝑥→∞ 26.) 𝑓(𝑥) = 2𝑥 2 − 3𝑥 + 1 ∞ _____ -∞ 𝑓(𝑥) → _____ 𝑥 → −∞ 𝑓(𝑥) → 28.) ℎ(𝑥) = 1 − 𝑥 6 𝑥→∞ -∞ _____ -∞ 31.) 𝑓(𝑥) = 6 − 2𝑥 + 4𝑥 2 − 5𝑥 3 𝑥→∞ -∞ _____ ∞ 𝑓(𝑥) → _____ 𝑥 → −∞ 𝑓(𝑥) → ∞ _____ ∞ 𝑓(𝑥) → _____ 𝑥 → −∞ 𝑓(𝑥) → 29.) 𝑓(𝑥) = −2.1𝑥 5 + 4𝑥 3 − 2 ℎ(𝑥) → _____ 𝑥 → −∞ ℎ(𝑥) → 𝑥→∞ 𝑥→∞ -∞ _____ ∞ 𝑓(𝑥) → _____ 𝑥 → −∞ 𝑓(𝑥) → 2 32.) ℎ(𝑡) = − 3 (𝑡 2 − 5𝑡 + 3) 𝑥→∞ ℎ(𝑡) → 𝑥 → −∞ ℎ(𝑡) → -∞ _____ -∞ _____ 7 27.) 𝑔(𝑥) = 5 − 2 𝑥 − 3𝑥 2 𝑥→∞ -∞ _____ -∞ 𝑔(𝑥) → _____ 𝑥 → −∞ 𝑔(𝑥) → 30.) 𝑓(𝑥) = 2𝑥 5 − 5𝑥 + 7.5 𝑥→∞ ∞ _____ -∞ 𝑓(𝑥) → _____ 𝑥 → −∞ 𝑓(𝑥) → 7 33.) 𝑓(𝑥) = − 8 (𝑠 3 + 5𝑠 2 − 7𝑥 + 1) 𝑥→∞ 𝑓(𝑠) → 𝑥 → −∞ 𝑓(𝑠) → -∞ _____ ∞ _____