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) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
[MA2015] AL2 (9-12) 29 : 29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]
Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
[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) 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) 23 : 23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
[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.