Question

use a vertical shift to graph the function. y = cos x + 10

Explanation:

Step1: Recall basic cosine graph

The basic cosine function is $y = \cos x$, which has an amplitude of 1, a period of $2\pi$, and it oscillates between - 1 and 1 with a mid - line at $y = 0$.

Step2: Identify the vertical shift

For the function $y=\cos x + 10$, the value of $10$ represents a vertical shift. The general form of a vertically shifted function is $y = f(x)+k$, where $k$ is the vertical shift. Here $k = 10$.

Step3: Determine the new characteristics

The mid - line of $y=\cos x$ which was at $y = 0$ is now at $y=10$. The amplitude remains 1, and the period remains $2\pi$. The function $y=\cos x + 10$ oscillates between $10 - 1=9$ and $10 + 1 = 11$.

Answer:

The graph of $y=\cos x$ is shifted 10 units up. It has a mid - line at $y = 10$, an amplitude of 1, and a period of $2\pi$, oscillating between $y = 9$ and $y = 11$.