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 negative 1, a point at negative 1 comma 0, and a point at 1 comma 0.
x g(x)
−4 6
−2 4
0 2
2 4
4 6

If g(x) = f(x) + k, what is the value of k?
k = −3
k = −2
k = 2
k = 3

Answer 1

(d) k = 3

Explanation:

Given the graph of the absolute value function f(x) = |x| -1, and a table of the function g(x) including the point g(0) = 2, you want the value of k if ...

g(x) = f(x) +k

Vertical translation

Using x = 0 in the equation, along with the values given in the problem statement, we have ...

g(x) = f(x) +k

g(0) = f(0) +k

2 = -1 +k . . . . . use given values of g(0), f(0)

3 = k . . . . . . . . add 1

The value of k is 3.

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