Question

I'm not sure how to answer this question. Could someone please help explain it?

Answer 1

Consider the parent function, $\displaystyle{ f(x)= \sqrt{x}$. 

The function f, takes a number x, and produces the square root of it, for example we have the points:

(1, 1), (4, 2), (25, 5), (100, 10).


The function $\displaystyle{ g(x)= \sqrt{x-5}$, takes a value x, subtracts it 5, and then produces the square root of this difference.


So to produce the values 1, 2, 5, 10 given in the previous function, we need to 

plug in the function not 1, 4, 25, and 100, but 6, 9, 30, 105.


Comparing  : (1, 1), (4, 2), (25, 5), (100, 10) of (x, f(x)) with 

                      (6, 1), (9, 2), (30, 5), (105, 10) of (x, g(x)),

we see that the graph of g is the same as the graph of f shifted 5 units right.



In general, the graph of  y=f(x-a), where a is a positive number, is the graph of y=f(x) shifted a units right.  

Answer: C