Question 8 (rubric) The parent graph, y = log b ( x ) is shown below. Match each

Question

Question 8 (rubric) The parent graph, y = logb(x) is shown below. Match each transformed function with its graph. Describe the transformation.




Graph 1 Before: After: Function:
A y = logb(x) + 3    
B y = logb(x) – 2                
C y = logb(x)    
D y = 2logb(x)    
E y = –3logb(x)     Description:


Graph 2 Before: After: Function:
A y = logb(x) + 3    
B y = logb(x) – 2    
C y = logb(x)    
D y = 2logb(x)    
E y = –3logb(x)                 Description:


Graph 3 Before: After: Function:
A y = logb(x) + 3    
B y = logb(x) – 2    
C y = logb(x)    
D y = 2logb(x)                
E y = –3logb(x)    

Graph 4 Before: After: Function:
A y = logb(x) + 3                
B y = logb(x) – 2    
C y = logb(x)    
D y = 2logb(x)    
E y = –3logb(x)     Description:


Graph 5 Before: After: Function:
A y = logb(x) + 3    
B y = logb(x) – 2    
C y = logb(x)                
D y = 2logb(x)    
E y = –3logb(x)     Description:

Explanation / Answer

Graph1 = log b(x) - 2

Graph2 = -3*log b(x)

Graph3 = 2*log b(x)

Graph4 = log b(x) + 3

Graph5 = [log b(x)]/4

You can determine these graph by these values:

using initial graph of log b(x)

when b(x) = 1, log b(x) = 0

when b(x) = 0, log b(x) = -infinity

when b(x) = 10, log b(x) = 1

Now in part 1

you can see that when

b(x) = 1, value of graph is -2 = 0 - 2 = log b(x) - 2

in part 2

when

b(x) = 0, value of graph is +infinity = -log b(x)

also when

b(x) = 10, value of graph goes toward -3, so function will be = -3*log b(x)

in part 3

b(x) = 10, value of graph goes toward 2, so function will be = 2*log b(x)

in part 4

you can see that when

b(x) = 1, value of graph is +3 = 0 + 3 = log b(x) + 3

in part 5

b(x) = 10, value of graph goes toward 1/4 or 0.25, so function will be = [log b(x)]/4

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