Presentation is loading. Please wait.

Presentation is loading. Please wait.

1-4: Patterns and Functions Essential Question:. 1-4: Patterns and Functions  A function is a relationship that assigns exactly one output value for.

Similar presentations


Presentation on theme: "1-4: Patterns and Functions Essential Question:. 1-4: Patterns and Functions  A function is a relationship that assigns exactly one output value for."— Presentation transcript:

1 1-4: Patterns and Functions Essential Question:

2 1-4: Patterns and Functions  A function is a relationship that assigns exactly one output value for each input value. For each input value, there is only one corresponding output.  A function rule, such as C = p p, is an equation that defines a functional relationship.

3 1-4: Patterns and Functions  Example 1: Writing a Function Rule  The relationship between the number of loads of laundry and cost is given below. Use the table to write a function rule.  Determine variable names to use  Let n = number of loadsLet c = cost  Determine the difference between successive entries.  $ $2.75 = $2.75$ $5.50 = 2.75 $11.00 – $8.25 = 2.75  Work backwards to determine if there would have been any cost with 0 loads.  Nope  c = 2.75 n

4 1-4: Patterns and Functions YY OUR T URN : Writing a Function Rule TThe relationship between the number of hours and the total miles driven is given below. Use the table to write a function rule. mm = 60 h

5  Example 2: Writing a Function Rule (with starting point)  The relationship between the number of houses built and number of toothpicks used.  Determine variable names to use  Let h = number of houses  Let t = number of toothpicks  Determine the difference between successive entries.  11 – 6 = 516 – 11 = 521 – 16 = 5  Work backwards to determine if there would have been any cost with 0 houses.  6 – 5 = 1  c = 5 n + 1

6 1-4: Patterns and Functions YY OUR T URN : Writing a Function Rule (with a starting point) TThe relationship between an input (x) and output (y) is given below. Determine the function for the data in the table. yy = 3x + 2

7  The relationship between the number of houses built and number of toothpicks used.  In this example, the number of toothpicks t depends on the number of houses h to be built.  This makes t the dependent variable, and h the independent variable.  In most real-world scenarios, the independent variable is the one you can control.

8 1-4: Patterns and Functions  Example 3  The cost of a memory stick is shown in the table below. Determine the dependent and independent variables.  Because the cost DEPENDS on the amount of memory you wish to purchase, the cost is the dependent variable  Because you control how much memory you wish to buy, memory is the INDEPENDENT variable.

9 1-4: Patterns and Functions  Your Turn  Determine the independent and dependent variable in the scenario below.  The cooking time for an unstuffed turkey is about 20 minutes per pound.  Dependent variable:  Independent variable: The cooking time The number of pounds to cook

10 1-4: Patterns and Functions  The possible values for input (or independent variable) of a function are the domain of the function. The possible values of the output (dependent variable) are the range of the function.  Example 4: Reasonable domain and range  Maria earns $7 an hour for babysitting after school and on Saturday. She works no more than 16 hours a week.  Identify the independent and dependent quantities  She controls the number of hours she works, so that is the independent variable.  The amount she earns is the dependent variable (her pay DEPENDS on the amount of hours she works)  Find a reasonable domain and range for this situation  She works no more than 16 hours a week, so a reasonable domain is anything from 0 to 16 hours.  A reasonable range is anything from $0 to $112 (7 16)

11 1-4: Patterns and Functions YYour Turn CCharlie downloads songs for $0.75 each. He has between $3.00 and $6.00 to spend on songs. IIdentify the independent and dependent variables. IIndependent variable: The amount of money he decides to spend DDependent variable: How many songs he downloads FFind a reasonable domain and range. DDomain: Anything from $3 to $6 RRange: Anything from 4 to 8 songs ( 3 / 0.75 and 6 / 0.75 )

12  Assignment  Practice Worksheet 1-4  All problems  Tomorrow  Quiz on Sections 1-1 through 1-3


Download ppt "1-4: Patterns and Functions Essential Question:. 1-4: Patterns and Functions  A function is a relationship that assigns exactly one output value for."

Similar presentations


Ads by Google