ATTRIBUTES OF EXPONENTIAL FUNCTIONS

Learn exponential function attributes: y-intercept, growth factor, and asymptote!

USE THE GRAPHS AND EQUATIONS BELOW TO ANSWER QUESTIONS 1 - 5. 1. Which of the following is the form a linear function should be written in? y=mx+b y=a(b)x y=ax2+bx+c 2. Which of the following is the form a quadratic function should be written in? y=mx+b y=a(b)x y=ax2+bx+c 3. Which of the following is the form an exponential function should be written in? y=mx+b y=a(b)x y=ax2+bx+c 4. Matching Graphs Match the following graphs with the type of function being represented. Linear Exponential Quadratic PARTS of an EXPONENTIAL FUNCTION Y-Intercept or Initial Amount The initial amount or y-intercept of an exponential function is the point where the graph crosses the y-axis. It is the "a" term in the equation. See the example below.Equation: y = 1(2)x a=1;y-intercept (0,1) 5. Identify the y-intercept for the graph below. (0,1) (0,4) (0,2) (0,10) 6. Identify the y-intercept for the graph below. (0,-1) (0,-4) (0,-2) (0,-10) 7. Identify the y-intercept for the graph below. (0,3) (0,5) (0,-2) (0,1) 8. Identify the y-intercept for the graph below. (0,1) (0,4) (0,2) (0,10) Growth/ Decay Factor the "b" term The growth rate is the "b" term in the exponential equation. It determines the rate at which the function will increase (grow) or decrease (decay).EXAMPLES: Exponential Growth or Decay? In the first column identify the growth rate, then in the second column determine if the function is an example of a growth or decay. EXPONENTIAL EQUATION GROWTH Rate? GROWTH OR DECAY? expo f(x) 2 GROWTH expo f(x) 0.5 DECAY expo f(x) 3 GROWTH expo f(x) 1 DECAY Exponential GROWTH or DECAYAn exponential growth function has a graph that is increasing from left to right.An exponential decay function has a graph that is decreasing from left to right. Match each graph below as an exponential GROWTH or exponential DECAY. Exponential Growth Exponential Decay Growth or Decay? Categorize each graph as an exponential growth or exponential decay graph. Growth Decay ASYMPTOTE An asymptote is a line that the function keeps getting close to but never actually touches. In the example above, the asymptote would be y = 2, because the curve(function) will never touch or cross Y= 2. 9. Identify the asymptote in the graph below. y = 1 y = - 2 y = 2 y = 0 10. Identify the asymptote in the graph below. y = 1 y = - 2 y = 2 y = 0 11. Identify the asymptote in the graph below. y = 1 y = - 2 y = 2 y = 0 12. Identify the asymptote in the graph below. y = 1 y = - 2 y = 2 y = 0