Question

PLEASE HELP
Write an equation for the function graphed above.

Answer 1

The equation of the graphed function is $y = 3\sec(\frac{\pi}{3}x) + 2$

How to determine the equation of the graph?

The graph is a secant graph, and it has the following form

$y = a\sec(bx) + c$

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:

$b = \frac{2\pi}{T}$

This gives

$b = \frac{2\pi}{6}$

Evaluate

$b = \frac{\pi}{3}$

Substitute the values of a, b and c in $y = a\sec(bx) + c$

$y = 3\sec(\frac{\pi}{3}x) + 2$

Hence, the equation of the graphed function is $y = 3\sec(\frac{\pi}{3}x) + 2$

Read more about graphs at:

https://brainly.com/question/4025726

#SPJ1