Write a cosine function that has a midline of y=5 an amplitude of 4,a period of 2, and a horizontal shift of 1 to the left. Answer Attemptiout of 2 f(x)=

The general form of a cosine function is $f(x) = A \cos(B(x - C)) + D$, where:<br />- $A$ is the amplitude,<br />- $B$ is the frequency,<br />- $C$ is the horizontal shift, and<br />- $D$ is the midline.<br /><br />Given that the midline is $y = 5$, the amplitude is 4, the period is 2, and the horizontal shift is 1 to the left, we can substitute these values into the general form of the cosine function.<br /><br />The amplitude $A$ is given as 4, so $A = 4$.<br /><br />The period of a cosine function is given by $\frac{2\pi}{B}$. We are given that the period is 2, so we can solve for $B$ as follows: $2 = \frac{2\pi}{B}$, which gives $B = \pi$.<br /><br />The horizontal shift $C$ is given as 1 to the left, which means $C = -1$.<br /><br />The midline $D$ is given as $y = 5$, so $D = 5$.<br /><br />Substituting these values into the general form of the cosine function gives $f(x) = 4 \cos(\pi(x + 1)) + 5$.