Graphs of direct and inverse variations

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

The graph does not pass through the origin (0,0) so this is neither a direct or inverse variation.

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

As x increase, y also increases and the function passes through the origin (0,0).
This is in the form of y = kx³

so y varies directly with x³

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

As x increase, y decreases. The function is linear and passes through the origin (0,0).
This is in the form of y = kx

so y varies directly with x but note the proportionality constant is negative; i.e. negative gradient.

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

As x increase, y decreases. The function is non-linear and passes through the origin (0,0).
This is in the form of y = kx³

so y varies directly with x³ but note the proportionality constant is negative; i.e. negative gradient.

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

The function is non-linear but no power of x with non-zero coefficient can produce y =0.
This is neither direct or inverse variation.

This graph shows _____ function.

• a direct variation

• an inverse variation

• neither a direct or inverse variation

Answer explanation

The function is non-linear and passes through the origin (0,0).
This is in the form of y = kx²

so y varies directly with x² but note the proportionality constant is negative; i.e. negative gradient.