1. Objective: TSW graph exponential functions and identify the domain and range of the function.

2.  A function is called an exponential function if it has a constant growth/decay factor.  An exponential functions graph contains an asymptote – a line the graph approaches BUT never crosses over (a barrier in the graph)

3.  Populations tend to growth exponentially not linearly.  When an object cools (e.g., a pot of soup on the dinner table), the temperature decreases exponentially toward the ambient temperature.  Radioactive substances decay exponentially.  Viruses and even rumors tend to spread exponentially through a population (at first).

4.  If the factor b is greater than 1, then we call the relationship exponential growth.  If the factor b is less than 1, we call the relationship exponential decay.  The equation for an exponential relationship is given by  y = ab x-h + k b = growth/decay factor b is ALWAYS the number with the exponent a = start amount If there is no “a” then a = 1 h = moves the graph left or right k = moves the graph up or down

5. 1. Identify the “k” value (this is your asymptote) - put a dotted line where your asymptote occurs. 2. Identify the “a” value and put your pencil on the y-axis (do not draw a point yet) 3. Use the “h” and “k” value to translate the graph from a. 4. Sketch the graph as either growth or decay. Exponential Growth Exponential Decay

6. 1. y = 0.25(3) x 2. f(x) = 5(0.5) x

7. 3. y = 0.75 x 4. f(x) = 4 x

8. 5. y = 2 x+2 - 3 6. y = 2(0.25) x-1 + 2

9. 7. y = 0.75 x+1 8. f(x) = 2(4) x + 3

10. pgs. 479-480 #’s 1-6(all), 8,13,15,16,18, 21-23(all)