Question

How is the graph of `h(x)=3+5/2x^2` related to the graph of `f(x)=x^2`?

Answer 1

The two functions when compared to each other on a graph constitute (or make) a straight line.

Explanation:

Consider the equation `h(x)=3+5/2x^2`
and the equation `g(x)=x^2`

Notice any terms which seem to be present in both equations?

The "`x^2`" term is present in both terms. While `h(x)` has another term (which is not a variable but a constant), `g(x)` is defined only by the term `x^2`.

So if we replace the `x^2` in the equation of `h(x)` with `g(x)`, we get

`h(x)=3+5/2g(x)`

Now, what's the equation for a straight line? Simple, it's

`y=c+mt` (usually `x` is written but I'm using `t` to avoid a confusion which will arise at first glance)

Notice anything similar between the two equations I just wrote down? Well, let's make it more simple to view then.

Well, if we took `h(x)=y` and `g(x)=t`

Now, it'll become `y=3+5/2t`

So there you have it. The functions `h(x)` and `g(x)` relate to each other as if they make a straight line.

Here's how they'll look if we drew them
graph{3+5/2x [-10, 10, -5, 5]}