Function Rules

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 ≠ 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 theteacher, the student haspartial 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.

x f(x)

-2

-1

0

1

2

f(-2) = 2(-2) + 3f(-2) = -1-1

f(-1) = 2(-1) + 3f(-1) = 1

1

f(0) = 2(0) + 3f(0) = 3

3

f(1) = 2(1) + 3f(1) = 5

5

f(2) = 2(2) + 3f(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).

x f(x)

-2 -1

-1 1

0 3

1 5

2 7

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) =

x f(x)

-2

-1

0

1

2

f(-2) = f(-2) = 0 0

f(-1) = f(-1) =

f(0) = f(0) = 2

2

f(1) = f(1) =

f(2) = f(2) = 0

0

Graph your table of values.

x f(x)

-2 0

-1

0 2

1

2 0

Your table of values become ordered pairs of (x, f(x)).

The ordered pairs are: (-2, 0), (-1, ), (0, 2), (1, ), (2, 0).

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) = x2.

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