What comes Next? Lesson 3.11

Sequence f To find the next term: Recursive Rule: To find the nth term: Explicit Rule: Arithmetic, Geometric, or Neither? + 0.6 to the previous term n F(n) 1 1.6 2 2.2 3 2.8 4 3.4 … F(1) = 1.6 ; F(n+1) = F(n) + 0.6 + 0.6 n times to 1 F(n) = 0.6n + 1 Arithmetic

Sequence g Geometric To find the next term: Recursive Rule: To find the nth term: Explicit Rule: Arithmetic, Geometric, or Neither? Multiply the previous term by 1 5 n G(n) 50 1 10 2 3 2 5 4 2 25 5 2 125 … G(1) = 10 ; G(n +1) = G(n) ∙ 1 5 Start with 50 and multiply 1 5 n times G(n) = 50 ( 1 5 ) 𝑛 Geometric

Sequence H To find the next term: Recursive Rule: To find the nth term: Explicit Rule: Arithmetic, Geometric, or Neither? Multiply the previous term by -0.2 n H(n) 5 1 -1 2 0.2 3 - 0.04 4 0.008 - 0.0016 … H(1) = -1 ; H(n+1) = H(n) ∙ -0.2 Start with 5 and multiply – 0.2 n times H(n) = 5 (- 0.2)n Geometric

Solve for y , graph and state Domain and Range 3x – 2y = 8 -3x -3x - 2y = -3x + 8 /-2 /-2 /-2 y = 3 2 x - 4 Domain: Range: All Real #s

Solve for y , graph and state Domain and Range All Real #s (0 , ∞) 4y – 4x = 0 + 4x + 4x 4y = 4x ( 1 4 )4y = 4x ( 1 4 ) y = 1 4 (4) 𝑥

Find the slope from two given points ( 2, 3 ) & (3, - 4) −4 −3 3 −2 −7 1 -7

Find the slope from two given points ( -2, -2 ) & (4, - 2) −2 −−2 4 −−2 0 6 0

Find the slope from two given points ( -5, 6 ) & (3, 8) 8 −6 3 −−5 2 8 1 4

End Behavior of Functions ∞ 𝐴𝑠 𝑥 → ∞ , 𝑓 𝑥 → ______ 𝐴𝑠 𝑥 →−∞, 𝑓 𝑥 → _______ ∞

End Behavior of Functions ∞ 𝐴𝑠 𝑥 → ∞ , 𝑓 𝑥 → ______ 𝐴𝑠 𝑥 →−∞, 𝑓 𝑥 → _______ −∞

End Behavior of Functions 𝐴𝑠 𝑥 → ∞ , 𝑓 𝑥 → ______ 𝐴𝑠 𝑥 →−∞, 𝑓 𝑥 → _______ ∞

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