Write a cosine function that has a midline of y=3 an amplitude of 4, a period of 2, and a horizontal shift of (1)/(2) to the right. Answer Attemptiout of 2 f(x)=

To write a cosine function with the given parameters, we need to use the general form of a cosine function:<br /><br />$f(x) = A \cos(B(x - C)) + D$<br /><br />where:<br />- $A$ is the amplitude<br />- $B$ is the frequency<br />- $C$ is the horizontal shift<br />- $D$ is the midline<br /><br />Given:<br />- Midline: $y = 3$, so $D = 3$<br />- Amplitude: 4, so $A = 4$<br />- Period: 2, so $B = \frac{2\pi}{2} = \pi$<br />- Horizontal shift: $\frac{1}{2}$ to the right, so $C = \frac{1}{2}$<br /><br />Substituting these values into the general form, we get:<br /><br />$f(x) = 4 \cos(\pi(x - \frac{1}{2})) + 3$<br /><br />Therefore, the cosine function that satisfies the given conditions is:<br /><br />$f(x) = 4 \cos(\pi(x - \frac{1}{2})) + 3$