the graph of the function y = 2x + cos x oscillates between two parallel lines. find the equations of the…
the graph of the function y = 2x + cos x oscillates between two parallel lines. find the equations of the lines and graph the lines and the function in the same viewing window. the top line is y = 2x + 1 and the bottom line is y = 2x - 1. (type equations. type your answers in slope - intercept form. use integers or decimals for any numbers in the equations.) choose the correct graph. all graphs are shown in a -2π,2π by -8,8 window.
Answer
Explanation:
Step1: Analyze range of cosine function
The range of $\cos x$ is $[- 1,1]$.
Step2: Find upper - bound line
When $\cos x = 1$, $y=2x+\cos x$ reaches its maximum value. So $y = 2x + 1$.
Step3: Find lower - bound line
When $\cos x=-1$, $y=2x+\cos x$ reaches its minimum value. So $y = 2x - 1$.
Step4: Consider graph characteristics
The function $y = 2x+\cos x$ is a linear - plus - cosine function. The lines $y = 2x + 1$ and $y = 2x - 1$ are parallel with slope $m = 2$. The function $y=2x+\cos x$ oscillates between these two lines.
Answer:
To choose the correct graph, look for a graph where the function $y = 2x+\cos x$ is a wavy line (due to the $\cos x$ term) that oscillates between the parallel lines $y = 2x + 1$ and $y = 2x - 1$ within the viewing window $[-2\pi,2\pi]$ by $[-8,8]$. Without seeing the actual details of graphs A, B, C, D, we can't definitively pick one, but the correct graph should have the function $y = 2x+\cos x$ (a line with wiggles) between the lines $y = 2x+1$ and $y = 2x - 1$. If we assume we have visually inspected and found the correct one based on these characteristics, we would state the letter of the correct graph. For example, if graph C is the one that meets the criteria, the answer would be C.