§111.C. High School
Page 14 October 2015 Update
higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for
analyzing complex situations, and use technology to build understanding, make connections
between representations, and provide support in solving problems.
(4) Statements that contain the word "including" reference content that must be mastered, while those
containing the phrase "such as" are intended as possible illustrative examples.
(c) Knowledge and skills.
(1) Mathematical process standards. The student uses mathematical processes to acquire and
demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
(2) Functions. The student uses process standards in mathematics to explore, describe, and analyze the
attributes of functions. The student makes connections between multiple representations of
functions and algebraically constructs new functions. The student analyzes and uses functions to
model real-world problems. The student is expected to:
(A) use the composition of two functions to model and solve real-world problems;
(B) demonstrate that function composition is not always commutative;
(C) represent a given function as a composite function of two or more functions;
(D) describe symmetry of graphs of even and odd functions;
(E) determine an inverse function, when it exists, for a given function over its domain or a
subset of its domain and represent the inverse using multiple representations;
(F) graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse
trigonometric, and piecewise defined functions, including step functions;
(G) graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial,
and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for
specific values of a, b, c, and d, in mathematical and real-world problems;
(H) graph arcsin x and arccos x and describe the limitations on the domain;
(I) determine and analyze the key features of exponential, logarithmic, rational, polynomial,
power, trigonometric, inverse trigonometric, and piecewise defined functions, including
step functions such as domain, range, symmetry, relative maximum, relative minimum,
zeros, asymptotes, and intervals over which the function is increasing or decreasing;
(J) analyze and describe end behavior of functions, including exponential, logarithmic,
rational, polynomial, and power functions, using infinity notation to communicate this
characteristic in mathematical and real-world problems;