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GSE Algebra I Unit 8 – Comparing and Contrasting Functions 8.3 - Comparing Functions Name: __________________________________________________________ Date: ____________________________ A. x y B. 0 4 1 12 2 20 C. This type of function has a constant rate of change. 3 28 D. Two Forms: y ax 2 bx c or y a x h k 2 E. This type of function has an asymptote. F. I. J. This type of function has a vertex and axis of symmetry K. x y N. O. This type of function has a common Ratio M. Arithmetic Sequence G. x 1 2 3 4 y 2 4 8 16 y=mx+b Write the letters of the functions or characteristics under the appropriate category. Linear: Quadratic: y ab H. x y x 1 2 3 4 500 100 20 4 L. 0 26 1 29 2 30 3 29 P. Geometric Sequences Write the equation for each of the tables (A, F, H, & K). Then write a story to describe it. A: F: H: Exponential: K: GSE Algebra I Unit 8 – Comparing and Contrasting Functions Exponential functions have a fixed number as the base and a variable number as the exponent. Let’s fill out the table to compare linear, quadratic and exponential functions over time. x Linear y = 2x + 2 8.3 - Comparing Functions Quadratic y = x2 + 2 Exponential y = 2x 0 1 2 3 4 5 1. Calculate and compare the slopes for each function from x1 = 0 to x2 = 1. Linear’s R.O.C Quadratic’s R.O.C. Exponential’s R.O.C. Whose R.O.C. is the steepest? 2. Calculate and compare the slopes for each function from x1 = 2 to x2 = 3. Linear’s R.O.C Quadratic’s R.O.C. Exponential’s R.O.C. Whose R.O.C. is the steepest? 3. Calculate and compare the slopes for each function from x1 = 4 to x2 = 5. Linear’s R.O.C Quadratic’s R.O.C. Exponential’s R.O.C. Whose R.O.C. is the steepest? VERY IMPORATANT TO KNOW! Conclusion over a LONG period of time the _______________________ function will exceed the value of the other functions. 4. Based on the graph on the right, which statement is not true? A. Functions f and g have the same x-intercept. B. The ordered pair (1, 2) is a solution for f(x). C. The ordered pair (2, 7) is a solution for g(x). D. The value of f(x) begins to exceed g(x) during the interval x = 1 and x = 2.