[MA2015] AL2 (9-12) 35 :
35 ) Find inverse functions. [F-BF4]
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse, and write an expression for the inverse. [F-BF4a]
Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
[MA2015] AL2 (9-12) 20 :
20 ) Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]
[MA2015] AL2 (9-12) 27 :
27 ) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]
[MA2015] AL2 (9-12) 31 :
31 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]
[MA2015] AL2 (9-12) 36 :
36 ) For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology. [F-LE4]
[MA2019] AL1-19 (9-12) 16 :
16. Compare and contrast relations and functions represented by equations, graphs, or tables that show related values; determine whether a relation is a function. Explain that a function f is a special kind of relation defined by the equation y = f(x). [MA2019] AL1-19 (9-12) 17 :
17. Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.
a. Use arithmetic operations to combine different types of standard functions to write and evaluate functions.
Example: Given two functions, one representing flow rate of water and the other representing evaporation of that water, combine the two functions to determine the amount of water in a container at a given time.
b. Use function composition to combine different types of standard functions to write and evaluate functions.
Example: Given the following relationships, determine what the expression S(T(t)) represents.
[MA2019] AL1-19 (9-12) 21 :
||Amount of studying: s
||Grade in course: G(s)
||Grade in course: g
||Amount of screen time: S(g)
||Amount of screen time: t
||Number of follers: T(t)
21. Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend from linear to quadratic, exponential, absolute value, and general piecewise.