Function Rules

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.

Use a rule to create a function displayed in a table.  Create a table using the domain {-2, -1, 0, 1, 2} for the rule f(x) = 2x + 3.  To do this, substitute each value of the domain into the rule. Then add the answer to the table. xf(x) f(-2) = 2(-2) + 3 f(-2) = -1 f(-1) = 2(-1) + 3 f(-1) = 1 1 f(0) = 2(0) + 3 f(0) = 3 3 f(1) = 2(1) + 3 f(1) = 5 5 f(2) = 2(2) + 3 f(2) = 7 7

Graph your table of values.  Your table of values become ordered pairs of (x, f(x)).  The ordered pairs are: (-2, -1), (-1, 1), (0, 3), (1, 5), (2, 7). xf(x)

Use a rule to create a function displayed in a table. xf(x)

Graph your table of values. xf(x)

Write a function to represent the data in the table.  Look at the x value. What operation or operations were used to change the x value to the f(x) value?  Once you decide on a rule, make sure it works for the other x values.  The rule is f(x) = x + 4.

Write a function to represent the data in table.  Look at the x value. What operation or operations were used to change the x value to the f(x) value?  Once you decide on a rule, make sure it works for the other x values.  The rule is f(x) = x 2.

Write a function to represent the real- world scenario.  The Museum of Science in Boston, MA has an exhibit called The Walk Through Computer. It is a scale model of a desktop computer. It is 20 times the size of a normal-sized desktop computer.  Write a function rule to describe the relationship between the normal-sized computer and the size of the exhibit.  f(x) = 20x  A space bar on a normal-sized computer is 4 3 / 8 inches long. How long is the space bar in the exhibit?  f( 35 / 8 ) = 20( 35 / 8 )  f( 35 / 8 ) = 87 ½ inches long  Or about 7 ¼ feet