P ATTERNS AND F UNCTIONS (L INEAR AND N ON - LINEAR ) Lessons 4-2 and 4-3

Height (feet) Time (Hours) 1. The graph to the left shows the height of a hot air balloon during a trip. What are the variables? Describe how they are related at various points on the graph Independent variable – time in hours Dependent variable – height of the balloon in feet The balloon lifts rapidly at a steady rate until it reaches a certain height. It then cruises for a period of time at this height. The last half of the flight is a slow, but steady descent back to the starting height. Warm – Up Questions

DRAMA CLUB Week1234 Total in Attendance The table shows the total number of people in attendance at a drama club after 1, 2, 3, and 4 weeks. Sketch a graph that could represent the data. Week Attendance

In a relationship between variables, the _____________________ variable changes in response to another variable, the _______________________ variable. Values of the independent variable are called ________________ (the ________________). Values of the dependent variable are called _____________ (the ________________). A _________________ ____________________ is a function whose graph is a nonvertical line or part of a nonvertical line. dependent independent domain x - values y - valuesrange linearfunction

Graph each set of ordered pairs. Use words to describe the pattern shown in the graph. This example is not linear because the dots do not form a straight line. It is a function (every x value is different.) This example is linear because the dots form a straight line. It is also a function (every x value is different.) This example is not linear because the dots do not form a straight line. It is not a function (the x value repeats).

Number of SquaresPerimeter n D. Using the diagram below, complete the table showing the relationship between the number of squares and the perimeter of the figure they form. Is this a function? Is it linear? n This relationship would be a function and it would be linear.

is a function that when graphed makes a nonvertical straight line line

Is it Linear or Non-Linear? Converting Inches to Centimeters E. Find the difference in consecutive pairs of x-values in the table and the difference for each consecutive pair of y-values. If the rations of the change in y compared to the change in x is consistent (the same) then the table represents a linear function Since each of the changes has a ratio of 2.54 to 1, this is a linear function.

16(4,16) 32(5,32) Not a linear function. The graph is not a straight line, and the ratio of the change in y divided by the change in x is not constant. G The ordered pairs (1, 1), (2, 8), (3, 27), (4, 64), and (5, 125) represent a function. What is a rule that represents this function? NOTE: This is not a linear function because it has an exponent of “3”. Linear functions do not have any exponents larger than “1”.