check the picture below.
notice, the dashed parts are the parts leftout, or outside the range for the piece-wise subfunction.
the red one has a solid dot on its tip, because x ⩽ 1 includes the 1, "less than OR equals to 1", the blue one, has a hole on its tip because it doesn't include the 1, x > 1.
anyhow, recall transformations, so the x³ - 4 is just x³ dropped by 4 units, and the x² + 3, is just x² moved up by 3 units.
