Answer:
[tex]f(x)=\frac{2}{\pi}(x-\pi)-4[/tex]
Step-by-step explanation:
Given: The function intersects its midline at [tex](\pi,-4)[/tex] and has a minimum point at [tex](\frac{\pi}{4} ,-5.5)[/tex]
To find: function f(x)
Solution:
Equation of a line joining points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Take [tex](x_1,y_1)=(\pi,-4)\,,\,(x_2,y_2)=(\frac{\pi}{4} ,-5.5)[/tex]
[tex]y+4=\frac{-5.5+4}{\frac{\pi}{4}-\pi }(x-\pi)\\ =\frac{-1.5(4)}{-3\pi}(x-\pi)\\ =\frac{2}{\pi}(x-\pi)\\[/tex]
[tex]f(x)=y=\frac{2}{\pi}(x-\pi) -4[/tex]
