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4G 4G 10:26 6 0 234 Domain and Range of Exponential Function Properties of exponential function and their graph Let f(x) = b*, b>0, and b# 1. 1. The domain is the set of real numbers (-co, co) 2. The range is the set of positive real numbers (0, co) 3. If b>1, f is an increasing exponential function 4. The function passes through the point (0, 1) because f(10) = b" - 1 5. The graph approaches but does not reach the x-axis. The x-axis a horizontal asymptote From property number 3, we know that y=2" is an increasing exponential function because b>1, and g(x)= =)*is a decreasing exponential function because 0 0} For g(x) = ( Domain : (x/x 69) Range: (y/ y > 0) y- intercepts: (0,1) X-intercept: NA Notice that the two graphs are symmetrical with respect to the y-axis, intersecting at (0, 1). The base of each function is the reciprocal of the other. 2. Graph f(x) = 2" and k(x) - -2" f(x) (x, f(x ) e(x) (x, g(x) 1/8 (-3, 1/8) -1/8 (-3, -1/8) (-2, X -1/4 (-2, -1/4 INHOHN W X (-1, X4) -1/2 (-1, -1/2) (0, 1) -1 (0, -1) (1, 2) -2 (1, -2) (2, 4) (2, 4) (3, 8) (3, -8) For h(x) = 2" Domain: [x/xed/ } Range: (y/y > 0) y-intercept: (0,1) For K(x) = -2 Domain: (x/x egt) Range: (y/y 0) y-intercept: (0,1) For q(x) = 5*+2 Domain: (x /xe )} Range: (y / y > 0} Intercept: (0, 3) REVISED KNOWLEDGE: Actual answer to the process questions/ focus questions. 1. How do you graph exponential function? . Given an exponential function of the form f (x) = b*, 1. Create a table of values. 2. Plot at least 3points from the table including the y-intercepts (0, 1) 3. Draw a smooth curve through this points. State the domain, ((-co, co), the range, (0, co) and the horizontal asymptote , y = 0. FINAL KNOWLEDGE: Generalization/ Synthesis/ Summary The graph of any exponential functions provides a visual representation of the behavior of its function values. Generally, exponential functions of the form f (x) = b*, where b is any positive real number other than 1, have the following characteristics: a. The domain is a set of real numbers. b. The range is the set of positive real numbers. c. The graph contains the point (0, 1). d. The graph is concave up. e. The function is increasing if b > 1 and decreasing if 0 1. 1. Domain: 2. Range: 3. Asymptote: x - intercept: . y - intercept: 6. Coordinates of the point common to the graph of f (x) = b*, for all b > 1: 7. Increasing or Decreasing: 8. One-to-one or not: Activity 2: Graphing exponential function: 1. Sketch the graph of f (x) = ()* and determine its properties