The graph of a sine function has an amplitude of 10, a midline of y = 4, and a period of 2. There is no phase shift. The graph is reflected over the x-axis. What is the equation of the function? f(x)=−10sin(π/2 x)+4 f(x)=−4sin(πx)+6 f(x)=−4sin(π/2 x)+6 f(x)=−10sin(πx)+4
+36916 REFLECTED sin fxn= - sinx
amplitude 10 = - 10 sin x
midline shifted up 4 = -10 sin x +4
period = 2 - 10 sin pi x +4
+128474 The original function has the form
f(x) = Asin (Bx) + C
A= the amplitude = 10
C = the midline shift = 4
B = 2pi / period = 2pi / 2 = pi
Original function is
f(x) = 10 sin (pi x) + 4
If this is reflected over the x axis.....then f(x) becomes -f(x) =
-10sin (pi x) - 4
See the original grah and the reflected graph here : https://www.desmos.com/calculator/gvwssl3gbf
