**Standard(s): **
[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*) =2*x*^{3} 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 *ab*^{ct} = *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.*

Function |
Input |
Output |

*G* |
Amount of studying: *s* |
Grade in course: *G(s)* |

*S* |
Grade in course: *g* |
Amount of screen time: *S(g)* |

*T* |
Amount of screen time: * t* |
Number of follers: *T(t)* |

[MA2019] AL1-19 (9-12) 21 : 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.**