Question

I’m so confused..? how do u write a function for this..?

Answer 1

`\boxed{y=h(x)=4x^2-5}`

Explanation:

Nonrigid transformations are those causing a distortion or a change in the shape of the original graph. Stretching a graph are part of nonrigid transformations. On the other hand, rigid transformations are those where the basic shape of the graph is unchanged. Translations are part of rigid transformations.

If
`y=f(x)` then
`g(x)=cf(x)` represents a vertical stretch if
`c>1`. In this case
`c=4`.

Since
`y=g(x)=x^2`, the:

• 
  `g(x)=4x^2` represents that the function is vertically stretched by a factor of 4

For translating a graph k units downward we have:

`\bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \ h(x)=f(x)-k`

Therefore,
`k=5` and translating the previous graph 5 units downward is:

`\boxed{y=h(x)=4x^2-5}`

Finally, this
`h(x)` is the function we are looking for.