The equation of the graphed function is [tex]y = 3\sec(\frac{\pi}{3}x) + 2[/tex]
How to determine the equation of the graph?
The graph is a secant graph, and it has the following form
[tex]y = a\sec(bx) + c[/tex]
From the graph, we have the following parameters:
- Local minimum = 5 i.e. the minimum y value in the upper quadrants
- Local maximum = -1 i.e. the maximum y value in the lower quadrant
- Time, T = 6 i.e. the difference between corresponding points on the curve
The amplitude (a) is calculated using:
a = 0.5 *(Local minimum - Local maximum)
a = 0.5 *(5 + 1) = 3
The vertical shift (c) is calculated using:
a = 0.5 *(Local minimum + Local maximum)
a = 0.5 *(5 - 1) = 2
The period (b) is calculated using:
[tex]b = \frac{2\pi}{T}[/tex]
This gives
[tex]b = \frac{2\pi}{6}[/tex]
Evaluate
[tex]b = \frac{\pi}{3}[/tex]
Substitute the values of a, b and c in [tex]y = a\sec(bx) + c[/tex]
[tex]y = 3\sec(\frac{\pi}{3}x) + 2[/tex]
Hence, the equation of the graphed function is [tex]y = 3\sec(\frac{\pi}{3}x) + 2[/tex]
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