ARM 10.53.523. CORE PLUS ALGEBRAIC AND FUNCTIONAL REASONING STANDARDS

(1) The functions, expressions, and inequalities content standards for high school are to: (a) 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); and (b) understand the relationship between a function and its inverse. (2) The polynomial functions content standards for high school are to: (a) understand polynomials are created by multiplying linear factors; (b) understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: (i) choosing the form strategically based on given information and intended use when writing an expression; (ii) converting between factored and standard form symbolically and using representations (e.g., area model); and (iii) interpreting the relationship between the factored form of the expression and the zeros of the function; (c) graph polynomial functions with and without the use of technology, by identifying zeros, relative maxima and minima, and end behavior; and (d) solve quadratic equations that have complex solutions, and understand why the solutions form a conjugate pair. (3) The exponential and logarithmic functions content standards for high school are to: (a) understand logarithmic functions as the inverse of exponential functions; (b) understand why e is defined as the natural base; (c) understand that exponential and logarithmic functions can be represented using multiple forms by: (i) expressing exponential functions in the form f(x)=ab^x and f(x)=Pe^(rt); and (ii) expressing logarithmic functions in base 10 and base e; (d) graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes, and end behavior; and (e) solve exponential and logarithmic equations using inverse operations with and without the use of technology. (4) The trigonometric functions content standards for high school are to: (a) understand how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers by: (i) defining the sine and cosine functions in terms of the unit circle; and (ii) defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine; (b) understand and use the radian measure of an angle, and convert between degree and radian measures; (c) graph trigonometric functions with and without the use of technology by: (i) graphing sine and cosine functions, identifying period, midline, and amplitude; and (ii) graphing tangent functions, identifying period and asymptotes; (d) solve trigonometric equations with and without the use of technology; and (e) apply the Law of Sines and the Law of Cosines to find unknown measurements in non-right triangles. (5) The modeling content standards for high school are to: (a) model situations in context with polynomial, exponential, logarithmic, and trigonometric functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: (i) determining if a set of data is best modeled by a polynomial, exponential, logarithmic, or trigonometric function or none, and explaining why; and (ii) understanding that there are contexts where solutions may not lie on the curve; (b) interpret the coefficients in a polynomial, exponential, logarithmic, and trigonometric model in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities; (c) use and interpret units correctly in modeling situations; and (d) choose a level of accuracy appropriate to limitations on measurement when reporting quantities in modeling situations.