Which answer choice describes how the graph of `f(x)=x^{2}` was transformed to create the graph of `h(x)=x^{2}-1`?

Question

a vertical shift up
a horizontal shift to the left
a vertical shift down
a horizontal shift to the right

Answer 1

To determine how the graph of \( f(x) = x^2 \) is transformed to create the graph of \( h(x) = x^2 - 1 \), let's analyze the transformation in the function forms.

The function \( h(x) = x^2 - 1 \) can be obtained by taking the function \( f(x) = x^2 \) and subtracting 1 from it.

This means that for every \( x \) value, the corresponding \( y \) value in \( h(x) \) is 1 unit less than the \( y \) value in \( f(x) \).

Graphically, this results in shifting the entire graph of \( f(x) = x^2 \) downwards by 1 unit.

Therefore, the correct answer choice is:
- a vertical shift down

So, the answer is:
- a vertical shift down