Question

Let f(z) = 8² and g(z) = 82+5 +1.

Which transformations are needed to transform the graph of f(z) to the graph of g (z)?
Select each correct answer.
horizontal translation 5 units right
vertical translation 5 units up
Overtical translation 1 unit up
O horizontal translation 1 unit left
O horizontal translation 5 units left
vertical translation 1 unit down
G3

Answer 1

To transform the graph of f(z) = 8² to g(z) = 8²+5 + 1, a vertical translation 1 unit up is needed. No horizontal translation is required.

Step-by-step explanation:

The student's question is about transforming the graph of a given function. In this case, we are comparing the functions f(z) = 8², a constant function equal to 64, and g(z) = 8^2+5 + 1, which simplifies to 64+6 since 8² is 64. To transform f(z) into g(z), we need the following transformations:

A vertical translation 1 unit up, because we are adding 1 to the outcome of f(z), resulting in the constant function g(z) = 65.

No horizontal translation is needed because the function is constant and does not depend on the variable z. Also, there is no vertical translation of 5 units because that is part of the computation within the function rather than an external transformation.