Question

The function g is defined as follows.g(x) = - 2x ^ 2 + 2If the graph of g is translated vertically downward by 5 units, it becomes the graph of a function f Find the expression for f(x)

Answer 1

The transformation rule that describes the translation vertically downwards by b units is given to be:

`f(x)\to g(x)-b`

The function is given to be:

`g(x)=-2x^2+2`

The graph of g(x) is translated downwards by 5 units. Hence:

`b=5`

Therefore, the expression for f(x) is gotten to be:

`\begin{gathered} f(x)=-2x^2+2-5 \\ f(x)=-2x^2-3 \end{gathered}`