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**Standard(s): **
[MA2015] AL2 (9-12) 14 :

[MA2015] AL2 (9-12) 31 :

[MA2019] AL1-19 (9-12) 16 :

*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.*

*Example: Given the following relationships, determine what the expression *S(T(t))* represents.*

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

14 ) Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* [A-SSE4]

Example: Calculate mortgage payments.

[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]

[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.

b. Use function composition to combine different types of standard functions to write and evaluate functions.

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) |

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.**

[MA2019] AL1-19 (9-12) 30 : 30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

b. Graph piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.