| Statement | Translation |
|---|
| f(0) = 0 | The point (0,0) is on the graph of f(x) |
| f'(1) = 0 | The slope of the tangent line at x = 1 is m = 0. This tangent line is horizontal |
| lim x->∞ f(x) = 0 | There is a horizontal asymptote at y = 0 |
| lim x->-∞ f(x) = 0 | There is a horizontal asymptote at y = 0 |
| lim x->-1 f(x) = ∞ | There is a vertical asymptote at x = -1 |
| f'(x)>0 on (-∞,-1)U(1,∞) | Function f(x) is increasing when x < -1 or when x > 1 |
| f'(x)<0 on (-1,1) | Function f(x) is decreasing when -1 < x < 1 |
| f"(x)>0 on (-∞,-1)U(-1,3) | Function f(x) is concave up when x < -1 or when -1 < x < 3 |
| f"(x)<0 on (3,∞) | Function f(x) is concave down when x > 3 |