Chapter 6, Problem 7CR

(a)

To determine

To graph: The function $y=x^2$

Explanation of Solution

Given information:

The function $y=x^2$

Graph:

To graph the function $y=x^2$ , find at least three points satisfying the function equation.

  $\begin{array}{cc}x& y=x^2\\ -2& 4\\ 0& 0\\ 3& 9\end{array}$

Plot these points on the graph and draw a smooth curve passing through it.

The graph of the function is

  

Interpretation:

The graph represents function of $y=x^2$

(b)

To determine

To graph: The function $y=x^3$

Explanation of Solution

Given information:

The function $y=x^3$

Graph:

To graph the function $y=x^3$ , find at least three points satisfying the function equation.

  $\begin{array}{cc}x& y=x^3\\ 1& 1\\ 0& 0\\ -1& -1\end{array}$

Plot these points on the graph and draw a curve passing through it.

The graph of the function is

  

Interpretation:

The graph represents function of $y=x^3$ .

(c)

To determine

To graph: The function $y=e^x$

Explanation of Solution

Given information:

The function $y=e^x$

Graph:

To graph the function $y=e^x$ , find at least three points satisfying the function equation.

  $\begin{array}{cc}x& y=e^x\\ 0& 1\\ 1& e=2.718\\ 2& e^2=7.389\end{array}$

Plot these points on the graph and draw a curve passing through it.

The graph of the function is

  

Interpretation:

The graph represents function of $y=e^x$

(d)

To determine

To graph: The function $y=\ln x$

Explanation of Solution

Given information:

The function, $y=\ln x$

Graph:

To graph the function $y=\ln x$ , find at least three points satisfying the function equation.

  $\begin{array}{cc}x& y=\ln x\\ 1& \ln \left(1\right)=0\\ 2& \ln \left(2\right)=0.693\\ 5& \ln \left(5\right)=1.609\end{array}$

Plot these points on the graph and draw a curve passing through it.

The graph of the function is

  

Interpretation:

The graph represents function of $y=\ln x$

(e)

To determine

To graph: The function $y=\sin x$

Explanation of Solution

Given information:

The function, $y=\sin x$

Graph:

To graph the function $y=\sin x$ , find at least three points satisfying the function equation.

  $\begin{array}{cc}x& y=\sin x\\ 0& \sin \left(0\right)=0\\ \frac{\pi }{2}& \sin \left(\frac{\pi }{2}\right)=1\\ -\pi & \sin \left(-\pi \right)=0\end{array}$

Plot these points on the graph and draw a curve passing through it.

The graph of the function is

  

Interpretation:

The graph represents function of $y=\sin x$

(f)

To determine

To graph: The function $y=\tan x$

Explanation of Solution

Given information:

The function $y=\tan x$

Graph:

To graph the function $y=\tan x$

Domain of $y=\tan x$ is $\left[n\pi ,\frac{\pi }{2}+n\pi \right)\cup \left(\frac{\pi }{2}+n\pi ,\pi +n\pi \right]$

That is, exclude the points from the domain which are multiples of $\frac{\pi }{2}$

Tangent function is the periodic function with period $\pi$

Also, the vertical asymptote of $y=\tan x$ is $\frac{\pi }{2}+n\pi$

Therefore, the graph of the function is

  

Interpretation:

The graph represents function of $y=\tan x$