[MA2015] AL1 (9-12) 32 :
32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [F-IF8a]
b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b]
Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as representing exponential growth and decay.
[MA2015] ALT (9-12) 13 :
13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
[MA2019] REG-8 (8) 3 :
3. Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2). [MA2019] AL1-19 (9-12) 24 :
24. Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.
a. Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.
b. Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. [MA2019] AL1-19 (9-12) 25 :
25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).