Question

Select the correct answer. Consider the function f(x) = 10x and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of f(x)? g ⁡ ( x ) = f ⁡ ( x − 6 ) = 10 ( x − 6 ) A. The graph of g(x) is the graph of f(x) shifted to the left 6 units. B. The graph of g(x) is the graph of f(x) shifted 6 units up. C. The graph of g(x) is the graph of f(x) shifted 6 units down. D. The graph of g(x) is the graph of f(x) shifted to the right 6 units.

Answer 1

Answer: D. the graph of g(x) is the graph of f(x) shifted to the right 6 units

Step-by-step explanation:

Answer 2

Answer: D

Explanation:

The function g(x) is obtained by shifting the function f(x) to the right by 6 units.

To see why, let's evaluate g(x) for some values of x:

g(x) = f(x - 6) = 10(x - 6)

If we substitute x = 6, we get:

g(6) = f(6 - 6) = f(0) = 10(0) = 0

This tells us that the point (6, 0) is on the graph of g(x).

If we substitute x = 12, we get:

g(12) = f(12 - 6) = f(6) = 10(6) = 60

This tells us that the point (12, 60) is on the graph of g(x).

Comparing these results with the graph of f(x) = 10x, we can see that the graph of g(x) is obtained by shifting the graph of f(x) 6 units to the right.

Therefore, the correct answer is D. The graph of g(x) is the graph of f(x) shifted to the right 6 units.