Question

Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 10, 0 and negative 8, 2. Group of answer choices 6 −3 −6 3

Answer 1

To determine the value of k, we need to observe the shift between the graphs of f(x) and g(x).

From the given information:
- The point (-4, 0) on f(x) corresponds to the point (-10, 0) on g(x).
- The point (-2, 2) on f(x) corresponds to the point (-8, 2) on g(x).

We can see that for each x-coordinate, the corresponding x-coordinate on g(x) is 6 units less than that on f(x).

Therefore, the value of k is -6.

In other words, g(x) = f(x - 6), which means that the graph of g(x) is obtained by shifting the graph of f(x) 6 units to the right.