Kw Domain and Range of Exponential Function Properties of exponential function and their graph Let f(x) = b', b>0, and bi 1. The domain is the set of real numbers (-00, 00) The range is the set of positive real numbers (0, 00) 3. lfb>1, f is an increasing exponential function 4. The function passes through the point (0, 1) because m0) = b = 1 _ 7;; S. The graph approaches but does not reach the xaxis. The x~axis a horizontal asymptote ; 1 : -~ _ 1. 2. From property number 3, we know that y=2x is an increasing exponential funconbeeaus'gbmd Eh): axis a decreasing exponential function because 0 0} For g(x) = (* Domain : (x/X E)?) 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) g(x) (x, g(x) 1/8 (-3, 1/8 1/8 (-3, -1/8) (-2, 34 ) 1/4 -2, -1/4) 1/2 (-1, 2 1/2 -1, -1/2) W N HOHN W X (0, 1 -1 (0, -1) (1, 2 ) - 2 (1, -2) 4 (2, 4) (2, -4) (3, 8) (3, -8) For h(x) = 2* Domain: (X/x 6/} Range: (y/y > 0} y-intercept: (0,1) For k(x) = -2* Domain: [x/x Et) Range: (y/ y 0} y-intercept: (0,1) For q(x) = 5*+2 Domain: (x /xE)1} 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) = bx, 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. 4. State the domain, ((-09, 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: 4. x - intercept: 5. 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. Activity 2 Big Task: Culminating Output: You are a designer in a clothing factory. One of your clients is a member of the Math Teacher of SVS, who requested for a print design of black T-shirt. The member of the organization will wear the T-shirt on their upcoming Math Culminating Activity. The design of the T-shirt should reflect the theme "Functions: Essential Tools in Understanding the Physical World." The following specifications must be met in the design.: a Front design: The theme and its visual representation b. Back design: the title, venue, and date of the culminating activity Title: Math Culminating Activity 60