Day 17 Classifying functions as linear, quadratic or exponential

Introduction It is always important to understand the nature and the structure of functions that we encounter in day to day life. This is necessary so that if a problem behaves like a given function, it becomes easier to solve and interpret the results based on the properties of the function at hand. In this lesson, we are concerned with linear, quadratic and exponential functions only.

Vocabulary:   This can be done in the notebooks or on vocabulary cards. Whatever system you use 

  This can be done in the notebooks or on vocabulary cards. Whatever system you use 

  This can be done in the notebooks or on vocabulary cards. Whatever system you use 

  This can be done in the notebooks or on vocabulary cards. Whatever system you use 

Get a tennis ball. Let one person have it in his/her hand Get a tennis ball. Let one person have it in his/her hand. Identify the direction in which the tennis ball will be gently thrown. Get other people, the observers, to stand some distance like 10 yards off the path of the tennis. Let the first per person through the ball gently at an angle not more than 45° along the horizontal.

Let the observers see the path created by the ball from the hand to the ground. a). Let every observer draw the path taken by the ball.

b). Identify the path taken. Quadratic function

2. Make a paper strip of 12 inches length 2. Make a paper strip of 12 inches length. Draw a table having two rows and 7 columns. In the first column, write cuts in the first row and ‘length (in)’ in the second row. In the second column, write 0 in the first row and 12 in the second row

Cut the paper into two equal lengths. Measure the length of one half Cut the paper into two equal lengths. Measure the length of one half. In the third column, write 1 in the first row and the measurement got in the second row. Take one piece (of length recorded in the second row third column) from the above step and cut it into two pieces and measure the length of the new half. In the fourth column, write 2 in the first row and the measurement of the new half in the second row.

a)Continues like that until you fill an eight column table. Cut 1 2 Length(in) 12 Cut 1 2 3 4 5 6 Length(in) 12  6 1.5 0.75 0.375 0.1875

b)Draw a graph of length (in) against the Cut.

c). Identify the kind of graph drawn. Exponential

  This can be done in the notebooks or on vocabulary cards. Whatever system you use 

EXAMPLE 2 Classify the following functions a). b). c). This can be done in the notebooks or on vocabulary cards. Whatever system you use 

a). Exponential function b). Quadratic function c). Linear function SOLUTION a). Exponential function b). Quadratic function c). Linear function This can be done in the notebooks or on vocabulary cards. Whatever system you use 

  This can be done in the notebooks or on vocabulary cards. Whatever system you use 

ANSWERS TO THE HOMEWORK 1. a). Linear function b). Quadratic function c). Quadratic function 2. Exponential function This can be done in the notebooks or on vocabulary cards. Whatever system you use 

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