PART 1 What is the effect on the graph of y log2 x 1 when

PART 1 What is the effect on the graph of y = log₂ (x + 1) when it is changed to y = log₂ (x – 5)? Explain why you chose your answer.

A The graph is vertically stretched.    
B The graph translates down the y-axis.    
C The x-intercept moves right on the x-axis.             
D The graph y = log₂ (x + 1) is reflected over the y-axis.    
Explanation:

I only   

I and II only   

I, II and III   

III only   

Explanation:

Solution

Part-1: y = log2(x+1) -----> y = log2(x-5)

Now , y = log2(x-5) can be written as y = log2(x +1 -6)

So, the first function y = log2(x+1) has been shifted horizontally by 6 units to right.

Option C x-intercept moves right on the x-axis

Part-2 : y = –4log5 (x + 5) – 6

Domain : x+5>0

x>-5

Y intercept : plug x=0

y = -4log5(5) -6 = -10

(0, -10)
the graph decreases with increasing value of x:

y = –4log5 (x + 5) – 6

So, Option I , II and III