  Using molecular dynamic simulations we study a family of continuous
core-softened potentials consisting of a hard core, a shoulder at closest
distances and an attractive well at further distance. The repulsive shoulder
and the well distances represent two length scales. We show that if the first
scale, the shoulder, is repulsive or has a small well, the potential has a
region in the pressure-temperature phase diagram with density, diffusion and
structural anomalies. However, if the closest scale becomes a deep attractive
well the regions in the pressure-temperature phase diagram where the three
anomalies are present shrink and disappear. This result enables us to predict
by the shape of the core-softened potential if anomalies would or would not be
present.
