Draw the graph of f : R → R, f (x) = x2 − 2.b By restricting the domain of f , form two one-to-one functions that have the samerule as f

To draw the graph of the function f(x) = x^2 - 2, you would follow these steps:

1. Identify the vertex of the parabola. The vertex form of a parabola is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. For the given function, the vertex is (0, -2).

2. Identify the axis of symmetry. For this function, the axis of symmetry is x = 0.

3. Choose some x values and find the corresponding y values to plot some points. For example, if x = -1, y = 1 - 2 = -1. If x = 1, y = 1 - 2 = -1. If x = -2, y = 4 - 2 = 2. If x = 2, y = 4 - 2 = 2.

4. Plot these points and draw a smooth curve through them to complete the graph.

To form two one-to-one functions that have the same rule as f, you can restrict the domain of f. One-to-one functions are functions where each x value corresponds to exactly one y value.

1. For the first function, restrict the domain to x ≤ 0. This will give you the function g(x) = x^2 - 2, for x ≤ 0.

2. For the second function, restrict the domain to x ≥ 0. This will give you the function h(x) = x^2 - 2, for x ≥ 0.

Both g(x) and h(x) are one-to-one functions that have the same rule as f.