T-QAD Day 12 @ 28 April 2020

Notes Topic: Functions

Subtopic: Absolute value functions

Example:

Given the absolute value function f(x)= | x -  3| ,
a) Sketch the graph of f(x) for the domain of  – 1 ≤ x ≤ 4 and 
     state the corresponding range of values of f(x). 
b) find the values of x that have the image of 10.

Solution :

a) Prepare a table:  f(x)= | x -  3|
 
    For x = -1,     | -1 - 3 |  = | - 4 |
                                        =  4

x	-1	0	1	2	3	4
f(x)	4	3	2	1	0	1

   You must make sure your graph touch the x-axis. To calculate it: 

    The f(y) = 0 at x-axis. So, 

                             | x - 3| = 0, 

                               x - 3  = 0

                                    x  = 3.

 Then sketch the graph...

 The corresponding range of values of f(x) is  0 ≤ f(x) ≤ 4. 

 Notes : the range of values of f(x) is the range from the lowest value 

               of y to the highest value of y covered by the graph.

b) Since it is given that the image of f(x) =10,

     

          f(x)   =  10

     |x - 3|   =  10

so,    x - 3  = 10    or x - 3 = -10

              x   = 13              x = - 7.

T-QAD for TODAY

Question 1 : Q1/D12/280420

Sketch the graph of f(x) = | 2x -5 | for the domain 0 ≤ x ≤  6   and state the 

corresponding range of  f(x)                                                                                                                          

                                                                                              (5 marks)

Question 2 : Q2/D12/280420

  The function of  f and g are defined by f(x) = | x - 2 |  and  g(x) = 2 - (x/3) respectively.

  a) On a piece of graph paper, draw the graph of y = f(x)      

       and y = g(x)  on the same axis  for - 1 ≤ x ≤  5

                                                                                                (6 marks)

  b) From your graphs, find the range of values of that satisfies the inequality 

       3 | 3 - 2 | ≤ 6 - x 

                                                                                                           (1 mark)

Answers T-QAD 27 April 2020

Check your answer and fill in the form to record your marks.

MyMarks