identify the graph of $y = x^3$.
identify the graph of $y = x^3$.
Answer
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. It passes through the origin ((0,0)). For ( x>0 ), ( y>0 ); for ( x<0 ), ( y<0 ). The graph has a cubic shape, increasing throughout its domain.
Step2: Analyze each graph
- Left graph: For ( x<0 ), ( y>0 ); for ( x>0 ), ( y<0 ). This is symmetric about the origin but the direction (sign of ( y ) for ( x ) sign) is reversed. Not ( y = x^3 ).
- Middle graph: For ( x<0 ), ( y\geq0 ); for ( x>0 ), ( y>0 ). It's not odd (symmetric about origin) as ( x<0 ) gives non - negative ( y ), while ( x^3 ) for ( x<0 ) is negative. Not ( y = x^3 ).
- Right graph: Passes through the origin. For ( x>0 ), ( y>0 ); for ( x<0 ), ( y<0 ), and has the cubic curve shape, symmetric about the origin, and increasing. Matches the properties of ( y = x^3 ).