1. (1) The functions content standards for high school are to:

   1. (a) interpret parts of an expression, such as terms, factors, and coefficients;
   2. (b) understand the definition of a function and distinguish between functions and relations;

   3. (c) represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically, by:

      1. (i) understanding that different representations highlight different aspects of functions, and choosing the representation that is appropriate for the context; and
      2. (ii) comparing properties of two functions, including when each is represented in a different way;
   4. (d) use function notation, evaluate functions, and interpret statements that use function notation in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities;
   5. (e) identify the domain and range of a function, including considering the constraints imposed by context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities;
   6. (f) understand that a graph of an equation in two variables is the set of all of its solutions plotted in a coordinate plane;
   7. (g) understand that expressions can be rewritten in equivalent forms to make different characteristics or features visible; and
   8. (h) rearrange literal equations to highlight quantities of interest.

2. (2) The linear functions content standards for high school are to:

   1. (a) understand that linear functions have a constant rate of change;
   2. (b) understand slope as a rate of change and y-intercept as initial value;

   3. (c) represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:

      1. (i) identifying the rate of change and initial value in each representation;
      2. (ii) converting between representations; and
      3. (iii) writing equations for a line perpendicular or parallel to a given line that passes through a given point;

   4. (d) understand that linear equations can be represented in multiple forms and the specific features of each form by:

      1. (i) choosing the form strategically when writing an equation based on given information and intended use;
      2. (ii) converting between slope-intercept, point-slope, and standard form symbolically;
      3. (iii) understanding the relationship between slope-intercept form, the rate of change, and the initial value;
      4. (iv) understanding the relationship between point-slope form, the rate of change, and a given point; and
      5. (v) understanding the relationship between standard form and the x- and y-intercepts;
   5. (e) understand that a solution to a system of equations is a coordinate pair that makes both equations true; and
   6. (f) solve systems of linear equations by graphing, substitution, and elimination, including systems with zero, one, or infinite solutions, while using technology and representations strategically.

3. (3) The quadratic functions and expressions content standards for high school are to:

   1. (a) understand that quadratic functions do not have a constant rate of change but have a constant second difference over equal intervals and identify the constant second difference in tables;
   2. (b) represent quadratic functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities;

   3. (c) understand that quadratic expressions can be represented in multiple forms and the specific features of each form by:

      1. (i) choosing the form strategically when writing an expression based on given information and intended use;
      2. (ii) converting between factored, standard, and vertex form symbolically and using representations;
      3. (iii) understanding the relationship between factored form and the zeros of the function; and
      4. (iv) understanding the relationship between vertex form and the vertex of the function;
   4. (d) solve quadratic equations by factoring, graphing, completing the square, using inverse operations, and the quadratic formula; use technology and representations strategically.

4. (4) The exponential functions and expressions content standards for high school are to:

   1. (a) understand that exponential functions have a constant common ratio over equal intervals, and identify the common ratio in tables and equations;
   2. (b) understand a as the initial value and b as the growth/decay factor for an exponential function written in standard form, y=a*b^x;
   3. (c) understand the relationship between growth/decay factor and growth/decay rate;
   4. (d) represent exponential functions using tables, graphs, equations, and verbal situations; using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities; and
   5. (e) solve exponential equations graphically, while using technology strategically.

5. (5) The modeling with functions content standards for high school are to:

   1. (a) model situations in context, with linear, quadratic, and exponential functions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:

      1. (i) determining if a set of data is best modeled by a linear function, quadratic function, exponential function, or none, and explaining why; and
      2. (ii) understanding that there are contexts where solutions may not lie on the curve;
   2. (b) interpret the coefficients in a linear, quadratic, and exponential model in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities;
   3. (c) choose and interpret measurement units in formulas, graphs, and data displays to understand problems and to guide problem-solving in modeling situations. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities; and
   4. (d) choose a level of accuracy appropriate to limitations on measurement when reporting quantities in modeling situations. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

Authorizing statute(s): Mont. Const. Art. X, sec. 9, 20-2-114, 20-7-101, MCA

Implementing statute(s): Mont. Const. Art. X, sec. 9, 20-2-121, 20-3-106, 20-7-101, MCA

History: NEW, 2025 MAR, 10-53-141, Eff. 7/1/26.