The data in the table can be modeled using the function y = A tan(Bx).
Input | output | input | output |
-8 | - infinity | 1 | 1.8 |
-7 | -44.2 | 2 | 3.6 |
-6 | -21.2 | 3 | 5.9 |
-5 | -13.2 | 4 | 8.8 |
-4 | -8.8 | 5 | 13.2 |
-3 | -5.9 | 6 | 21.2 |
-2 | -3.6 | 7 | 44.2 |
-1 | -1.8 | 8 | infinity |
0 | 0 |
1. State the value of A.
a. 11.3
b. 7
c. 4.7
d. 3.1
2. State the location of asymptotes.
a. 16k, k € Z
b. 8 + 4k, k € Z
c. 8k, k € Z
d. 8 + 16k, k € Z
3. Use the model to evaluate the function at x = 10.
a. -6.6
b -15.9
c. -21.2
d. -9.9
The data in the table can be modeled using the function y = A tan(Bx).
I am going to assume that this question is in degrees.
Two of the asymptotes lie at \(x=\pm \frac{90}{B}\)
The asymptotes here lie at x= 8 and x= -8
So
8=90/B
B=90/8 = 11.25
I think the first question actually meant for you to find B not A.
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Now one asymptote is at x=-8 then x=8 so the next one will be at x=8+16=24
So
the asymptotes occur at x=8+16K where k is an integer.
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3. Use the model to evaluate the function at x = 10.
f(10)=f(-6)=-21.2
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Here is the graph, maybe it will help you though it was not necessary for answering those questions.