What operations indicate a horizontal translation?
Rule for g: g(x) = (x-2)^3 - 4 Transformation: Translation right by 2 units.
Practice makes perfect
We will describe the graph of g as a transformation of the graph of f. Then we will write a rule for g.
Describing the Transformation
Horizontal translations mean addition or subtraction from the argument of a function. Translating right is subtracting, and translating left is adding.
Horizontal Translations
Translation right h units, h>0
y=f(x- h)
Translation left h units, h>0
y=f(x+ h)
In this case, we are translating the graph of f right by 2 units. Therefore, we will subtract 2 from the input.
g(x)=f(x) right by 2 units
⇓
g(x)=f(x- 2)
Finding the Rule for g(x)
Let's write the rule for g. To do so, we will substitute x-2 for x in the rule for f.
g(x)=x^3-4 ⇒ g( x-2)=( x-2)^3-4
Therefore, we have that f(x)=(x-2)^3-4.
