Question

`y = {x}^(2) + 3`I need help to find the parent function, Type of Translation, Domain, and Range for the equation above.

Answer 1

The given function is

`y=x^2+3`

It's important to know that parent functions are the simplest form of a function. In this case, the parent function would be

`y=x^2`

Notice that the given function has a 3 as an independent term, this means the function is being shifted 3 units up, that's the transformation. This transformation is a translation.

On the other hand, the domain is all real numbers because it's a quadratic function.

`D\colon(-\infty,\infty)`

However, the range is restricted because this function is represented by a parabola which has a turning point at its vertex. In this case, the turning point is at (0,3), the y-interception. So, the range is all real numbers greater than or equal to 3.

`R\colon\lbrack3,\infty)`

There you have it!