Question

The graphs of f(x) and g(x)= f(x)+k are shown below. the value of k is ____​

Answer 1

The value of k is 2

Explanation:

The rule of vertical translation

• If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k ⇒ add y-coordinate of every point by k

• If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k ⇒ subtract y-coordinate of every point by k

From the graph

∵ Point (0, 0) ∈ f(x)

∵ Point (0, 2) ∈ g(x)

∵ Point (2, 4) ∈ f(x)

∵ Point (2, 6) ∈ g(x)

∴ Each y-coordinates of the points on f(x) added by 2 on g(x)

→ That means f(x) is translated up 2 units

∴ f(x) is translated up by 2 units

→ By using the first rule above

∴ g(x) = f(x) + 2

∵ g(x) = f(x) + k

∴ k = 2

∴ The value of k is 2