Using the concept of the tangent function, it is found that:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
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Tangent function:
It is given by:
[tex]f(x) = \tan{Bx}[/tex]
- The period is [tex]P = \frac{\pi}{|B|}[/tex].
- The frequency is [tex]F = \frac{1}{P} = \frac{|B|}{\pi}[/tex].
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- The period is inversely proportional to B, thus, as B increases, the period decreases.
- Frequency is inversely proportional to the period, thus, as the period decreases, the frequency increases.
- When B is negative, we get [tex]f(x) = \tan{-Bx} = f(-x)[/tex], thus, the function is reflected over the y-axis, as the graph at the end of the answer shows, with f(x) is red(B positive) and f(-x) in blue(B negative).
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Considering the three bullet points above, the correct option is:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
A similar problem is given at https://brainly.com/question/16828446
