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Function Rules for Graphs Learning Goal for Focus 3 (HS.A-CED.A.1, HS.F-IF.A.1 & 2, HS.F-IF.B.4 & 5): The student will understand the concept of a function and use of function notation. 4 3 2 1 0 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand the concept of a function and use of function notation. - Evaluate functions for given inputs. - Interpret key features of graphs and tables of a function. - Sketch graphs of functions. - Determine the domain of the equation or graph of a function and what it may represent in context. - Convert a table, graph, set of ordered pairs, or description into function notation by identifying a rule. - Identify numbers that are not in the domain of a function. [f(x) = 1/x x≠ 0 or f(x) = 𝑥 x ≠ a negative] The student will be able to understand the concept of a function. - Correctly use function terminology (domain, range, f(x)). - Determine if a relationship given in a table, graph, or words depicts a function. With help from the teacher, the student has partial success with function terminology, function notation and determining if a relation table or graph depict a function. Even with help, the student has no success understanding the concept of a function. Make graphs from a function… Graph the function f(x) = 2x – 3. Start by making a table of values. Graph the ordered pairs. Connect the dots. x f(x) -2 -7 -5 -3 -1 1 -1 0 1 2 Write a function from a graph. Step 1: Find where the line will cross the yaxis. (0, 2) Step 2: Is the line going up or down? Up = positive slope Down = negative slope Step 3: Calculate the slope. Find two points on the line. Count the number of spaces up or down (numerator). Count the number of spaces to the right (denominator). Reduce the fraction = this is the slope of the line. 2 1 Step 4: Write the function: 2=2 1 f(x) = (slope)(x) + (where it crosses the y-axis) f(x) = 2x + 2 Write a function from a graph. Step 1: Find where the line will cross the yaxis. (0, 0) Step 2: Is the line going up or down? Up = positive slope Down = negative slope Step 3: Calculate the slope. Find two points on the line. Count the number of spaces up or down (numerator). Count the number of spaces to the right (denominator). Reduce the fraction = this is the slope of the line. 1 3 Step 4: Write the function: -1 3 f(x) = (slope)(x) + (where it crosses the y-axis) f(x) = -1/3x Write a function from a graph. Step 1: Find where the line will cross the yaxis. (0, -2) Step 2: Is the line going up or down? Up = positive slope Down = negative slope Step 3: Calculate the slope. Find two points on the line. Count the number of spaces up or down (numerator). Count the number of spaces to the right (denominator). Reduce the fraction = this is the slope of the line. 3 2 Step 4: Write the function: -3 2 f(x) = (slope)(x) + (where it crosses the y-axis) f(x) = -3/2x - 2