Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s
2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the
function from a description of a relationship or from two (x, y) values,
including reading these from a table or from a graph. Interpret the rate
of change and initial value of a linear function in terms of the situation
it models, and in terms of its graph or a table of values.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Intermediate, 8th Grade
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and
data displays.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
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.★
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end
behavior.
Subject Area: Mathematics (NYS P-12 Common Core)
Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
