Question

The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. x g(x) −1 5 0 4 1 3 2 2 3 3 If g(x) = f(x + k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2

Answer 1

To find the value of k, we need to determine the horizontal shift of f(x) to match g(x). Since g(x) = f(x + k), we need to find the value of k such that when x + k equals -1, f(x) equals 3, and when x + k equals 1, f(x) equals 5.

Step-by-step explanation:

In this question, we are given a graph of the function f(x) and a table describing the absolute value function g(x). We are asked to find the value of k if g(x) = f(x + k).

From the graph, we can see that the vertex of f(x) is at (0, 2), and there are two points on the graph at (-1, 3) and (1, 3). From the table, we can see that g(x) takes the value of 5 when x = -1, and 3 when x = 1.

To find the value of k, we need to determine the horizontal shift of f(x) to match g(x). Since g(x) = f(x + k), we need to find the value of k such that when x + k equals -1, f(x) equals 3, and when x + k equals 1, f(x) equals 5.

As the given points on the graph of f(x) have the same y-value as the corresponding points on g(x), we can see that the value of k is -2.