Function Rules for Graphs

43210 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 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. 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.

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. xf(x)

Write a function from a graph.  Step 1: Find where the line will cross the y- axis.  (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.  Step 4: Write the function:  f(x) = (slope)(x) + (where it crosses the y-axis)  f(x) = 2x = 2 1

Write a function from a graph.  Step 1: Find where the line will cross the y- axis.  (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.  Step 4: Write the function:  f(x) = (slope)(x) + (where it crosses the y-axis)  f(x) = - 1 / 3 x 1 3 3

Write a function from a graph.  Step 1: Find where the line will cross the y- axis.  (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.  Step 4: Write the function:  f(x) = (slope)(x) + (where it crosses the y-axis)  f(x) = - 3 / 2 x