Question

5 Describe the transformations performed on the graph of f(x) = x² to obtain the graph of g(x)when g(x) = (x − 3)² — 4.

Answer 1

Solution:

Given:

$\begin{gathered} f(x)=x^2 \\ g(x)=(x-3)^2-4 \end{gathered}$

The transformations that occurred are;

$\begin{gathered} x^2\text{ to }(x-3)^2\text{ shows a horizontal shift of 3 units to the right.} \\ (x-3)^2\text{ to }(x-3)^2-4\text{ shows a vertical shift 4 units down} \end{gathered}$

The graph of the two functions showing the transformations is shown;

Therefore, the transformations performed on the graph of f(x) to obtain g(x) are;

Vertical Shift 4 units down.

Horizontal Shift 3 units right.