Answer:
The options C and D both are correct.
Explanation:
One function is f(x) = x ..... (1) and another function is g(x) = f(x) -5 = x - 5 .......(2)
Now, for x = 0, f(x) = 0 and g(x) = -5
So, the y-intercepts are not the same.
Now, f'(x) = 1 and g'(x) is also 1.
Hence, the rate of change of both functions is the same.
Since the slope of equations (1) and (2) are same which is 1, then we can conclude that the functions are parallel to each other.
If we put x = 1, then f(1) = 1 and g(1) = -4. Again f(2) = 2 and g(2) = 2 - 5 = -3
Hence, for each fixed value of x the value of g(x) is 5 less than the value of f(x).
So, the graph of the function f(x) is translated down by 5 units to produce f(x) - 5.
Therefore, the options C and D both are correct. (Answer)