## Standards of Learning (SOL)

 Essential Knowledge and Skills

• Determine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function. (a)
• Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically. (b, c, d)
• Use the x-intercepts from the graphical representation of a quadratic function to determine and confirm its factors. (c, d)
• For any value, x, in the domain of f, determine f(x). (e)
• Represent relations and functions using verbal descriptions, tables, equations, and graph. Given one representation, represent the relation in another form. (f)
• Investigate and analyze characteristics and multiple representations of functions with a graphing utility. (a, b, c, d, e, f)

## Resources

Vocabulary
Linear, quadratic, functions, relation, domain, range, zeros, intercepts, elements, tables, graphs, equations, dependent variable, input, output, ordered pair, x-intercept, y-intercept, equivalent, real number, root, factor, set notation

## Vertical Articulation

Prior Standard of Learning
8.15 The student will determine whether a given relation is a function; and determine the domain and range of a function.

Post Standard of Learning

AFDA.1 The student will investigate and analyze linear, quadratic, exponential, and logarithmic function families and their characteristics. Key concepts include domain and range; intervals on which a function is increasing or decreasing; absolute maxima and minima; zeros; intercepts; values of a function for elements in its domain; connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; end behavior; and vertical and horizontal asymptotes.

AII.7 The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include domain, range, and continuity; intervals in which a function is increasing or decreasing, extrema; zeros; intercepts; values of a function for elements in its domain; connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; end behavior; vertical and horizontal asymptotes; inverse of a function; and composition of functions, algebraically and graphically.

 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.
 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.
 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.

## Essential Questions

• What is the difference between a relation and a function?
• What are the different ways functions can be represented?
• How can you determine whether a relation is a function when given a set of ordered pairs, a table, or a mapping?
• How can you determine whether a relation is a function when given a graph?
• How can you identify the domain and range of a function?
• How can you identify the zeros of a function?
• How can you identify the intercepts of a function?
• How can you use the x-intercepts from a quadratic function to determine its factors?
• How can you find f(x) for a given value or set of given values of x?
• How can you represent relations and functions using verbal descriptions, tables, equations, and graphs?
• How do you investigate characteristics of functions with a graphing utility?