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Warm-Up for Section 3.5B Simplify: 1. 2.

Warm-Up for Section 3.5B Simplify: 1. 2. Let f ( x ) = 2 x + 9 and g ( x ) = 3 x – 1. Perform the indicated operation and state the domain. 3. 4. f ( x ) – g ( x ) 5. g ( f (x)) Solve. 6. 2 x – 1 = 8 2 x + 1 . Warm-Up 3.5B Answers 1. 2.

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Warm-Up for Section 3.5B Simplify: 1. 2.

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  1. Warm-Up for Section 3.5B Simplify: 1. 2. Let f(x) = 2x + 9 and g(x) = 3x – 1. Perform the indicated operation and state the domain. 3. 4. f(x) – g(x) 5. g(f(x)) Solve. 6. 2x – 1 = 82x + 1

  2. Warm-Up 3.5B Answers 1. 2. 3. 4. y = –x +10 5. y = 6x + 26 all reals all reals all reals except x = -9/2 6.

  3. Warm-up 3.5B Work 1. 2. 3. 4. y = 2x + 9 – (3x – 1) 5. g(2x + 9) y = 2x + 9 – 3x + 1 = 3(2x + 9) – 1 all reals excepty = -x + 10 = 6x + 27 – 1 x = -9/2all realsy = 6x + 26 all reals 6.

  4. 3.4B Homework Answers 1. x = 2 2. all reals 3. x = 1 4. x = 7 5. x = 1 6. x = 1 7. x ≥ 7 8. x ≤ 1 9. x< 4 10. x ≥ 2 11. x ≤ 6 12. x ≤ 6 13. x = 1 14. x = 3 15. x = 2 16. x ≤ 1 17. x ≤ 1 18. x ≥ 2

  5. Exponential Growth and Decay Section 3.5B Standard: MM2A2 bce Essential Question: How do you graph and analyze exponential functions and their inverses?

  6. Vocabulary: Exponential function: a function of the form y = abx where a ≠ 0 and the base b is a positive number other than 1 Exponential decay function: a function of the form y = abx where a > 0 and 0 < b < 1 Exponential growth function: a function of the form y = abx where a > 0 and b > 1 Growth or decay factor: b in the function y = abx Asymptote: a line that a graph approaches more and more closely End behavior: the behavior of the graph as x approaches positive and negative infinity.

  7. 8 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 1) Graph y = 3x. Growth

  8. Domain: Range: Asymptotes: Zeros: y-intercept: Interval of increasing: Interval of decreasing: Rate of change (-2 ≤ x ≤ 2) End behavior: All reals y > 0 y = 0 None (0, 1) All reals None (-2, 1/9) (2, 9) L: x → -∞, y→ 0; R: x → ∞, y → ∞

  9. 8 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 2) Graph . Decay

  10. Domain: Range: Asymptotes: Zeros: Y-intercept: Interval of increasing: Interval of decreasing: Rate of change (-2 ≤ x ≤ 2) End behavior: All reals y > 0 y = 0 None (0, 1) None All reals (-2, 9) (2, 1/9) L: x→ -∞, y → ∞; R: x→ ∞, y → 0

  11. 8 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 3) Graph . Growth

  12. Domain: Range: Asymptotes: Zeros: Y-intercept: Interval of increasing: Interval of decreasing: Rate of change (1 ≤ x ≤ 2) : End behavior: All reals y > -2 y = -2 Between 1 and 2 (0, -1⅔) All reals None (1, -1) (2, 1) L: x→ -∞, y → -2; R: x→ ∞, y → ∞

  13. 8 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 4) Graph . Decay

  14. Domain: Range: Asymptotes: Zeros: y-intercept: Interval of increasing: Interval of decreasing: Rate of change (0 ≤ x ≤ 1) : End behavior: All reals y > 1 y = 1 None (0, 10) None All reals (0, 10) (1, 4) x → -∞, y → ∞; x → ∞, y → 1

  15. For an exponential function of the form y = bx, a. If b > 1, then the function is increasing throughout its domain. b. If 0 < b < 1, then the function is decreasing throughout its domain. Determine if the function is increasing or decreasing throughout its domain: (5). g(x) = 3x + 5 (6). h(x) = 2.5x (7). p(x) = (½)-x (8). (9). (10). increasing increasing increasing increasing increasing decreasing

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