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The vertical asymptote requires a factor of (x-4) in the denominator.
The double zero requires a factor of (x-1)² in the numerator.
At x=0, these factors will give a value of (-1)²/(-4) = -1/4, so another constant factor of -12 is needed to make the y-intercept be 3.
Your rational function is ...
... y = -12(x -1)²/(x -4)
The domain and the range are 0 ≤ ∅ ≤ 2π and -1 ≤ cos(∅) ≤ 1, respectively.
<h3>The domain and the range</h3>The domain is the set of input values i.e. the ∅ values.
On the table, we can see that the ∅ value is from 0 to 2π.
This means that the domain is 0 ≤ ∅ ≤ 2π
On the other hand, the range is the set of output values i.e. the cos(∅) values.
On the table, we can see that the cos(∅) value is from -1 to 1.
This means that the range is -1 ≤ cos(∅) ≤ 1
Hence, the domain and the range are 0 ≤ ∅ ≤ 2π and -1 ≤ cos(∅) ≤ 1, respectively.
<h3>The points on a graph</h3>See attachment 1
<h3>The graph of the function</h3>See attachment 2
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