Functions in the REAL World

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.

Review:Find the domain and range of the function:

x f(x)

3 5

5 -2

6 -4

10 -12

12 -15

x f(x)

0 10

-9 8

3 10

4 -5

-12 -15

Domain: {3, 5, 6, 10, 12}Range: {5, -2, -4, -12, -15}

Domain: {0, -9, 3, 4, -12}Range: {10, 8, 10, -5, -15}

Find the domain of the function: f(x) = 3x + 9

The domain is any real number. D = {all real numbers}

f(x) = You can’t take the square root of a negative

number. The domain is any real number ≥ 5. D = {All real numbers ≥ 5 }

f(x) = The denominator cannot equal zero. The domain is any real number except 4. D = {All real numbers 4}

Find the domain and range of the function:

The temperature in a house drops 2°F for every hour the air conditioner is on between the hours 6:00 am and 11:00 am. The following is a list of times and temperatures in the house: 6 am, 82°F; 8 am 78°F; 9 am 76°F; 10 am, 74°F, and 11 am, 72°F.

Domain: {6, 8, 9, 10, 11} Range: {82, 78, 76, 74, 72}

Find the domain of the function:

If the function f(n) represents the number of hours required to construct n pizzas at dinner time at the local delivery joint, what domain makes sense?

You can’t make negative pizzas or partial pizzas. Domain: {whole numbers ≥ 0}

Find the domain of the function: Your cell phone plan charges you $0.20 for each text

message you send. Your parents put a cap of $50 on your texting bill each month. If f(x) = 0.2x is the cost of the total number of texts you send per month, what is the domain of the function?

First find the maximum amount of texts you can send each month by substitute 50 in where f(x) is. 50 = 0.2x x = 250 You cannot go over 250 texts.

Can you have negative text messages? Write the domain. Domain: {0 ≤ x ≤ 250}