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 wind the top line is and the bottom line is (type equations. type your answers in slope - intercept form. use integers or decimals for any numbers in the equations )
Answer
Explanation:
Step1: Recall the range of cosine function
The range of $y = \cos x$ is $[- 1,1]$.
Step2: Find the upper - bound line
To find the upper - bound line, we consider the maximum value of $\cos x$. When $\cos x=1$, the function $y = 2x+\cos x$ has the maximum value for a given $x$. So $y_{max}=2x + 1$.
Step3: Find the lower - bound line
To find the lower - bound line, we consider the minimum value of $\cos x$. When $\cos x=-1$, the function $y = 2x+\cos x$ has the minimum value for a given $x$. So $y_{min}=2x - 1$.
Answer:
The top line is $y = 2x+1$ and the bottom line is $y = 2x - 1$