Write a cosine function that has a midline of y=5 an amplitude of 3, a period of pi 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 $y=5$, which means the function will be shifted vertically so that its center is at $y=5$.<br /><br />2. Amplitude: The amplitude is the distance between the midline and the maximum or minimum value of the cosine function. In this case, the amplitude is 3, which means the function will have a maximum value of $5+3=8$ and a minimum value of $5-3=2$.<br /><br />3. Period: The period is the length of one complete cycle of the cosine function. In this case, the period is $\pi$, which means the function will repeat every $\pi$ units along the x-axis.<br /><br />4. Horizontal shift: A horizontal shift moves the graph of the function left or right. In this case, the function is shifted $\frac{\pi}{4}$ to the right, which means we need to subtract $\frac{\pi}{4}$ from the argument of the cosine function.<br /><br />Putting all these together, we can write the cosine function as:<br /><br />$f(x) = 3\cos\left(x-\frac{\pi}{4}\right) + 5$<br /><br />This function has a midline of $y=5$, an amplitude of 3, a period of $\pi$, and a horizontal shift of $\frac{\pi}{4}$ to the right.