Question

2b.) What transformation of f(x) does y correspond to?

a.) a verticle translation 4 units down
b.) a verticle translation 4 units up
c.) a horizontal translation 4 units to the left
d.) a horizontal translation 4 units to the right

Answer 1

The transformation is " a horizontal translation 4 units to the right " ⇒ (d)

Explanation:

Let us revise the translation of a function

• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)

• If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

• If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

• If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k

Let us look at the graph and choose some points on the f(x) and find their images on y

∵ Point (1, 2) lies on f(x)

∵ Point (5, 2) lies on y

∵ Point (3, 8) lies on f(x)

∵ Point (7, 8) lies on y

→ There is no change in the y-coordinates of the points, the change

only in the x-coordinates

∴ The translation is horizontally

∵ 5 - 1 = 4 units ⇒ positive value means to right

∴ f(x) is translated 4 units to the right

∴ The answer is " a horizontal translation 4 units to the right " (d)