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1.5 – Exponential Functions. Basic Definitions Exponential Function where a > 0 and a ≠ 1. With translations:

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Presentation on theme: "1.5 – Exponential Functions. Basic Definitions Exponential Function where a > 0 and a ≠ 1. With translations:"— Presentation transcript:

1 1.5 – Exponential Functions

2 Basic Definitions

3 Exponential Function where a > 0 and a ≠ 1. With translations:

4 Natural Exponential Function where e is the natural base and e  2.718…

5 Try This Functionf(x) = 2 x h(x) = (0.5) x g(x) = e x Domain Range Increasing or Decreasing Point Shared On All Graphs (-∞, ∞) (0, ∞) Inc. Dec.Inc. (0, 1)

6 Properties of f (x) = a x Domain: Range: Increasing for: Decreasing for: Point Shared On All Graphs: Asymptote: (-∞, ∞) (0, ∞) a > 1 0 < a < 1 (0, 1) y = 0

7 Graph Sketching Use translation of functions to graph the following. Determine the domain and range of each. 1. f (x) = -5 (x + 2) – 3 2. g(x) = (1 / 3) (x – 1) + 2

8 Try This Determine the values of x for which 2 x > x 4. Write your answer using interval notation. You may use your graphing calculator.

9 Try This An isotope of sodium, 24 Na, has a half-life of 15 hours. A sample of this isotope has mass 2 g. (a)Find the amount remaining after 60 hours. (b)Find the amount remaining after t hours. (c)Estimate the amount remaining after 4 days. (d)Use a graph to estimate the time required for the mass to be reduced to 0.01 g.

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