Question

Write a function g whose graph represents the indicated transformation of the graph of f.

f(x) = 3x ; translation 5 units up

the translated function is g(x) =

Answer 1

g(x) = 3x +5

Explanation:

You want the function that results from translating f(x) = 3x upward by 5 units.

Translation

The y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.

The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:

(x, f(x) +5) . . . . . graph translated 5 units up

Using the given definition of f(x), this becomes ...

(x, 3x +5)

The translated function is defined as g(x), so we have ...

(x, g(x)) = (x, 3x +5)

or ...

g(x) = 3x +5