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Which answer describes the transformation of f(x)=x2−1 to g(x)=(x−1)2−1 ?




a vertical translation 1 unit up


a horizontal translation 1 unit to the left


a vertical translation 1 unit down


a horizontal translation 1 unit to the right

Verified Answer :

a horizontal translation 1 unit to the right

f(x) x-intercept = 0.5
g(x) x-intercept = 0.5 + 1

Answer:

The answer that describes the transformation f(x) tog(x) is:

               a horizontal translation 1 unit to the right

Step-by-step explanation:

We are given a parent function f(x) as:

              \(f(x)=x^2-1\)

and the transformed function g(x) is given by:

               \(g(x)=(x-1)^2-1\)

We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively.

Here we  have: a= -1

This means that the shift is to the right by 1 units.

In other words we may say that the transformation is a horizontal translation 1 units to the right.

 

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