Write a cosine function that has a midline of y=5 an amplitude of 4,a period of (pi )/(2) , and a horizontal shift of (pi )/(4) to the right. Answer Attemptiout of 2 f(x)=

To write a cosine function with the given parameters, we need to consider the following:<br /><br />1. Midline: The midline is the horizontal line that runs through the center of the cosine function. In this case, the midline is $y = 5$.<br /><br />2. Amplitude: The amplitude is the distance from the midline to the maximum or minimum value of the cosine function. In this case, the amplitude is 4.<br /><br />3. Period: The period is the distance between two consecutive points where the cosine function repeats itself. In this case, the period is $\frac{\pi}{2}$.<br /><br />4. Horizontal shift: The horizontal shift moves the cosine function left or right. In this case, the horizontal shift is $\frac{\pi}{4}$ to the right.<br /><br />Using these parameters, we can write the cosine function as:<br /><br />$f(x) = 4 \cos\left(2x - \frac{\pi}{2}\right) + 5$<br /><br />This function has a midline of $y = 5$, an amplitude of 4, a period of $\frac{\pi}{2}$, and a horizontal shift of $\frac{\pi}{4}$ to the right.