AR.3

Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, f(x) = x, f(x) = x^2, f(x) = √x, f(x) = 1/x, f(x) = x^3, f(x) = 3√x, f(x) = b^x, f(x) = |x|, and f(x) = logb (x) where b is 10 or e; functions and their inverses; and key attributes of these functions.

AR.3.ACompare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions such as a set comprised of a linear, a quadratic, and an exponential function or a set comprised of an absolute value, a quadratic, and a square root function tabular, graphically, and symbolically.AR.3.BCompare and contrast the key attributes of a function and its inverse when it exists, including domain, range, maxima, minima, and intercepts, tabular, graphically, and symbolically.AR.3.CVerify that two functions are inverses of each other tabular and graphically such as situations involving compound interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius conversions.AR.3.DRepresent a resulting function tabular, graphically, and symbolically when functions are combined or separated using arithmetic operations such as combining a 20% discount and a 6% sales tax on a sale to determine h(x), the total sale, f(x) = 0.8x, g(x) = 0.06(0.8x), and h(x) = f(x) + g(x).AR.3.EModel a situation using function notation when the output of one function is the input of a second function such as determining a function h(x) = g(f(x)) = 1.06(0.8x) for the final purchase price, h(x) of an item with price x dollars representing a 20% discount, f(x) = 0.8x followed by a 6% sales tax, g(x) = 1.06x.AR.3.FCompare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.
Goblins

1-on-1 AI tutoring aligned to AR.3. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →