Algebra 1 Glencoe McGraw-Hill JoAnn Evans Functions & Discrete vs Continuous Data Algebra 1 Glencoe McGraw-Hill JoAnn Evans

What does “B” represent? the blood flow to the brain at the time of injury D C About what % of blood flow occurs 2 days after a concussion? B about 78% What does the % of blood flow depend on? the number of days after the injury

The return of normal blood flow is a function of the number of days that have followed since the concussion. In other words, the % of blood flow depends on the number of days that have passed since the concussion.

In a function, the x values are called the input of the function…… y In a function, the x values are called the input of the function…… and the y values are called the output of the function. The output depends on the input. y is the dependent variable x x is the independent variable

Indentify independent and dependent variables: In Phoenix, the average amount of electricity rises as the daily average temperature increases and falls as the daily average temperature decreases. Independent::::::::::the temperature Dependent:::::::::::::electricity used The amount of electricity depends on the temperature increases or decreases.

Indentify independent and dependent variables: One way to estimate the distance of a thunderstorm is to count the number of seconds that pass from the sight of a flash of lightning until the sound of thunder is heard. (Divide that number by 5 to get the approximate distance in miles of the storm). Independent::::::::::seconds counted Dependent:::::::::::::distance of the storm The distance of the storm depends on the number of seconds counted after the sight of lightning in this estimation.

Indentify independent and dependent variables: It takes about 40 gallons of sap from maple trees to make 1 gallon of maple syrup. Independent::::::::::gallons of sap Dependent:::::::::::::gallons of maple syrup The amount of syrup made depends on the amount of sap used.

Interpreting the Meaning of Graphs Without a Scale independent variable: time dependent variable: rainfall total rainfall The rain steadily increases, decreases until it stops, then starts and stops again. time The graph represents the amount of rainfall during a storm. Identify the independent and dependent variable. Describe what’s happening in the graph.

height time independent variable: time dependent variable: height The tsunami slowly increases at first, then quickly rises. time The graph represents the height of a tsunami as it approaches shore. Identify the independent and dependent variable. Describe what’s happening in the graph.

number of questions answered independent variable: time dependent variable: # of questions answered number of questions answered The student answers a question, stops to think, then answers another, and repeats. time The graph represents a student taking an algebra test. Identify the independent and dependent variable. Describe what’s happening in the graph.

account balance in $ time independent variable: time dependent variable: $ in account account balance in $ time The graph represents the balance of a savings account over time. Identify the independent and dependent variable. Describe what’s happening in the graph.

height time independent variable: time dependent variable: height The graph represents the height of a baseball after it’s hit. Identify the independent and dependent variable. Describe what’s happening in the graph.

The # of books is the independent variable. (x) Draw a Graph At the No Tax Bookstore for every two books you buy at the regular price of $15 each, you get a third book free. # of books 1 2 3 4 5 6 total cost in $ $15 $30 $30 $45 $60 $60 The # of books is the independent variable. (x) The cost depends on the number of books purchased, so it’s the dependent variable. (y)

There are no values between the points. y A function like this is called a discrete function. In a discrete function the points aren’t connected. There are no values between the points. . . Cost of books 90 . 75 . . 60 . 45 30 15 x 1 2 3 4 5 6 Number of books (1, 15) (2, 30) (3, 30) (4, 45) (5, 60) (6, 60)

(1, 15) (2, 30) (3, 30) (4, 45) (5, 60) (6, 60) The set of ordered pairs that represents the information in the previous graph is called a relation. The set of the first numbers in the ordered pairs is called the domain of the function. The set of the second numbers in the ordered pairs is called the range of the function.

(1, 15) (2, 30) (3, 30) (4, 45) (5, 60) (6, 60) Domain: {1, 2, 3, 4, 5, 6} Range: {15, 30, 45, 60} Knowing the domain and range of the function will allow you to plan the scale for a graph. The x-values go up by one each time, so it would make sense to number the x-axis by ones. The y-values go up by 15, so numbering the y-axis in multiples of 15 would be a good choice.

A function graphed with a straight line or a smooth curve is called a continuous function.