Chapter 8.5, Problem 33AYU

In Problems 25-32, use the method of adding $y\text{-coordinates}$ to graph each function.

$f(x)=x+\cos x$

To determine

To graph: The function using the method of adding y coordinates.

Answer to Problem 33AYU

Explanation of Solution

Given:

$f\left(x\right) = x + \text{cos}x$

Graph:

Graph of $f\left(x\right) = x + \text{cos}x$

The graph for $f\left(x\right) = x + \text{cos}x$ using the method of adding y coordinates is plotted above. The set of points obtained by substitution are shown below.

$\begin{array}{llllll}\text{x}\hfill & 0\hfill & \text{π}/2\hfill & \text{π}\hfill & 3\text{π/2}\hfill & 2\text{π}\hfill \\ \text{y} = \text{x}\hfill & 0\hfill & \frac{\text{π}}{2}\hfill & \text{π}\hfill & \frac{3\text{π}}{2}\hfill & 2\text{π}\hfill \\ \text{Cosx}\hfill & 1\hfill & 0\hfill & - 1\hfill & 0\hfill & 1\hfill \\ \text{f}(\text{x})\hfill & 1\hfill & 1.57\hfill & 2.14\hfill & 4.71\hfill & 7.28\hfill \end{array}$

Points for graph (0, 1), ( $\frac{\text{π}}{2},$1.57), (π, 2.14), ( $\frac{3\text{π}}{2}$, 4.71), (2π, 7.28)