Question

Let f(x) = 3x^2 + 2.

The equation g(x) is f(x) translated up 5 units.
What is the equation of g(x)?​

Answer 1

g(x) = 3x² + 7

Explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Here the translation is 5 units up, thus

g(x) = 3x² + 2 + 5 = 3x² + 7

Answer 2

g(x) = 3x² + 7

Explanation:

To translate a function upward by b units, we add the constant b to the function.

Thus, g(x) =ƒ(x) +5 = 3x² +2 + 5 = 3x² + 7

The figure below shows the graphs of ƒ(x) and g(x). The graph of g(x) is the same as that of ƒ(x) shifted up by 5 units.