If f(x)=x^2-1, describe in words what f(x)-4 would do to the graph of f(x).

Question

Please help. I do not understand.

Answer 1

Consider a graph with the y-axis as vertical, and the x-axis as horizontal. Treat f(x) as y. You graph y=x²-1

It's the standard parabola, opening upwards, with vertex at the origin,(0,0), but shifted down by one unit, so the vertex is (0,-1).

If you have y=x²-4, it shifts the parabola down by 4 units, so the vertex, the minimum point, is (0,-4)

It shifts the x²-1 parabola down by 3 units to x²-4. Every point on the graph is shifted downward by 3 units from the original graph.

Or shifted down by 4 units from the parabola y=x²

Alternatively, you could think of keeping the parabola in exactly the same position, and shift the x-axis upwards by 3 units