Question

Given `f(x)=x^2 - 7`, how do you describe the transformation?

Answer 1

the graph of function f is downward shift of 3 units.

Explanation:

suppose that `y=g(x)`
one of the coordinates include (a,b)

then if `y=g(x)+c`
then the coordinates becomes (a,b+c)

when c>0 the graph is upward shift of c unit
when c<0 the graph is downward shift of c unit.
the transformation of here is a vertical translation.

note that `f(x)` is a quadratic function.
so when `f(x)=x^2`
the graph should look like this
graph{x^2 [-10, 10, -5, 5]}

so now since `f(x)=x^2-3`
so the graph look like this.
graph{x^2-3 [-10, 10, -5, 5]}

the graph of function f is downward shift of 3 units.