Given: A seventh-degree polynomial function has zeros of -6, 0 (multiplicity of 2), 1, and 4 (multiplicity of 3).
Required: To determine the behavior of the graph at the zeros.
Explanation: The given seventh-degree polynomial can be represented as
[tex]\left(x+6\right)\left(x-0\right)^2\left(x-1\right)(x-4)^3[/tex]
Now, the graph will cross straight through at x=-6 and x=1.
We have an odd multiplicity at x=4; hence the graph will cross through while hugging.
We have an even multiplicity at x=0; therefore, the graph will be tangent.
Here is the graph of the given function-
Final Answer: The graph will cross straight through at x=-6 and x=1,
the graph will cross through while hugging at x=4,
the graph will be tangent at x=0.
