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Answer:
- asymptotes: x=±6, y=0; zero: x=0
- 20 blue fish
Explanation:
1. The vertical asymptotes are where the denominator is zero.
x² -36 = 0
(x -6)(x +6) = 0 ⇒ x = 6 or x = -6 . . . vertical asymptotes
The horizontal asymptote is the function value when x is large. Since the numerator is lower degree than the denominator, the ratio becomes near 0 as x gets large. The horizontal asymptote is y = 0.
The function value is zero when the numerator is zero:
6x = 0 ⇒ x = 0 . . . . the zero of the function
A function graph is attached, with vertical asymptotes and zero shown.
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2. You can work this problem by considering the ratios.
If 60% of fish are red, then 40% are blue. The difference in numbers is 60% -40% = 20% of the total number of fish. That difference is 10 fish.
The number of blue fish is 40% of the total, which is 2×20% = 2×10 fish.
There are 20 blue fish.