Answer:
6. C. the degrees are the same
7. B. the leading coefficients are the same
Step-by-step explanation:
6.
The hole at x=-1 suggests a denominator factor of (x+1) that is canceled by a numerator factor of (x+1).
The vertical asymptote at x=2 means there is a denominator factor of x-2.
The horizontal asymptote of y=0 means there are no values of x such that f(x)=0.
The curve will not have this shape unless the difference in degrees between numerator and denominator is odd (and there is only one real zero in the denominator function). That is, the degrees of numerator and denominator cannot be the same.
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7.
The graph appears to be described by something like ...
y = (3/x) -3 = (3 -3x)/x
The degrees of the numerator and denominator are the same, which is why there is a non-zero horizontal asymptote.
The leading coefficient in the numerator is -3; in the denominator, 1. So, the leading coefficients are not the same.
The function has a zero at x=1, so the numerator must be zero there.
If there are common factors in the numerator and denominator, they would only show in this graph if they had real zeros. None such are indicated, so we assume there are no common factors in numerator and denominator.
