Administrative Rules of Montana › Department 10 - EDUCATION › Chapter 10.53 - CONTENT STANDARDS › Subchapter 10.53.5 - Mathematics Content Standards › Rule 10.53.514 - MONTANA HIGH SCHOOL MATHEMATICS FUNCTIONS STANDARDS

Current through Register Vol. 13, July 5, 2024
(1) Mathematics functions: interpreting
				functions content standards for high school are:
(a) understand that a function from one set
				(called the domain) to another set (called the range) assigns to each element
				of the domain exactly one element of the range; if f is a function and x is an
				element of its domain, then f(x) denotes the output of f corresponding to the
				input x; and the graph of f is the graph of the equation y = f(x);
(b) use function notation, evaluate functions
				for inputs in their domains, and interpret statements that use function
				notation in terms of a context;
(c)
				recognize that sequences are functions, sometimes defined recursively, whose
				domain is a subset of the integers; for example, the Fibonacci sequence is
				defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n
				[GREATEREQUAL] 1;
(d) for a
				function that models a relationship between two quantities, interpret key
				features of graphs and tables in terms of the quantities and sketch graphs
				showing key features given a verbal description of the relationship; key
				features include: intercepts; intervals where the function is increasing,
				decreasing, positive, or negative; relative maximums and minimums; symmetries;
				end behavior; and periodicity;*
(e) relate the domain of a function to its
				graph and, where applicable, to the quantitative relationship it describes; for
				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;*
(f) calculate and interpret the average rate
				of change of a function (presented symbolically or as a table) over a specified
				interval and estimate the rate of change from a
				graph;*
(g) graph functions expressed symbolically
				and show key features of the graph, by hand in simple cases and using
				technology for more complicated cases;*
(i) graph linear and quadratic functions and
				show intercepts, maxima, and minima;
(ii) graph square root, cube root, and
				piecewise-defined functions, including step functions and absolute value
				functions;
(iii) graph polynomial
				functions, identifying zeros when suitable factorizations are available, and
				showing end behavior;
(iv) (+)
				graph rational functions, identifying zeros and asymptotes when suitable
				factorizations are available and showing end behavior; and
(v) graph exponential and logarithmic
				functions, showing intercepts and end behavior, and trigonometric functions,
				showing period, midline, and amplitude;
(h) write a function defined by an expression
				in different but equivalent forms to reveal and explain different properties of
				the function;
(i) use the process of
				factoring and completing the square in a quadratic function to show zeros,
				extreme values, and symmetry of the graph and interpret these in terms of a
				context; and
(ii) use the
				properties of exponents to interpret expressions for exponential functions; for
				example, identify percent rate of change in functions such as y =
				(1.02)t, y = (0.97)t, y =
				(1.01)12t, y = (1.2)t/10
				and classify them as representing exponential growth or decay; and
(i) compare properties of two
				functions each represented in a different way (algebraically, graphically,
				numerically in tables, or by verbal descriptions); for example, given a graph
				of one quadratic function and an algebraic expression for another, say which
				has the larger maximum.