Question

identify the graph of $y = x^3$.

Explanation:

Step1: Recall properties of \( y = x^3 \)

The function \( y = x^3 \) is an odd function, so its graph is symmetric about the origin. Also, when \( x>0 \), \( y>0 \); when \( x<0 \), \( y<0 \).

Step2: Analyze each graph

• First graph: For \( x<0 \), \( y>0 \) (since it's above the x - axis), which does not satisfy \( y = x^3 \) (as for \( x<0 \), \( x^3<0 \)). So this is not the graph of \( y = x^3 \).
• Second graph: For \( x>0 \), \( y<0 \) (below the x - axis), which does not satisfy \( y = x^3 \) (as for \( x>0 \), \( x^3>0 \)). So this is not the graph of \( y = x^3 \).
• Third graph: For \( x>0 \), \( y>0 \); for \( x<0 \), \( y<0 \), and it is symmetric about the origin. This matches the properties of \( y=x^3 \).

Answer:

The Right Graph (the third graph from the left)