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 1, a point at negative 1 comma 2, and a point at 1 comma 2. x g(x) −4 0 −2 −2 0 −4 2 −2 4 0 If g(x) = f(x) + k, what is the value of k? k = −5 k = −4 k = 4 k = 5

Answer 1

(a) k = -5

Explanation:

You want to know the value of k in g(x) = f(x) +k given that point (0, -4) lies on the graph of g(x) and point (0, 1) lies on the graph of f(x).

Vertical translation

Filling in the vertex values, we have ...

g(x) = f(x) +k

g(0) = f(0) +k

-4 = 1 +k

-5 = k . . . . . . . subtract 1

The value of k is -5.

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