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Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of

Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rate of change. An exponential function is a function of the form.

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Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of

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  1. Exponential FunctionsMM3A2eInvestigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rate of change.

  2. An exponential function is a function of the form where a is a positive real number (a > 0) and . The domain of f is the set of all real numbers.

  3. (1, 6) (1, 3) (-1, 1/6) (-1, 1/3) (0, 1)

  4. Summary of the characteristics of the graph of a >1 • The domain is all real numbers. Range is set of positive numbers. • No x-intercepts; y-intercept is 1. • The x-axis (y=0) is a horizontal asymptote as a>1, is an increasing function and is one-to-one. • The graph contains the points (0,1); (1,a), and (-1, 1/a).

  5. (-1, 6) (-1, 3) (0, 1) (1, 1/3) (1, 1/6)

  6. Summary of the characteristics of the graph of 0 <a <1 • The domain is all real numbers. Range is set of positive numbers. • No x-intercepts; y-intercept is 1. • The x-axis (y=0) is a horizontal asymptote as 0<a<1, is a decreasing function and is one-to-one. • The graph contains the points (0,1); (1,a), and (-1, 1/a). • The graph is smooth continuous with no corners or gaps.

  7. (1, 3) (0, 1)

  8. (-1, 3) (0, 1)

  9. (-1, 5) (0, 3) y = 2

  10. Domain:All real numbers Range: { y | y >2 } or Horizontal Asymptote:y = 2

  11. Domain: (-∞,∞) y-intercept is the point (0,1) Continuous Increasing if a > 1 Range: (0,∞) No x-intercept Horizontal asymptote y=0 Decreasing if a < 1 Characteristics of Exponential Functions f(x) = ax

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