Question

How will you sketch the graph of the given function with respect to the x-axis?

y=x(x-1)³

A. tangent at both (1,0) and (0,0)
B.crossing (1,0) and tangent to (0,0)
C.tangent at (1,0) and crossing (0,0)
D.crossing both (1,0) and (0,0)

2.How will you sketch the graph of the given function with respect to the x-axis?

y=x(x-1)⁴

A.tangent at both (1,0) and (0,0)
B.crossing (1,0) and tangent to (0,0)
C.tangent at (1,0) and crossing (0,0)
D.crossing both (1,0) and (0,0)

Answer 1

determine what the roots are by setting the function equal to 0

from there, determine the multiplicity of the roots. if the root has an odd exponent, crosses the line at the root. if a root has an even exponent, it is tangent to the root.