Chapter 1.4, Problem 32E

To determine

Identify the changes in graph when $c$ changes.

Answer to Problem 32E

The graph changes with $c$ .

Explanation of Solution

Given information:

Graph the function $f\left(x\right)=\sqrt{1+c{x}^2}$ for several values of $c$ . How does the graph change when $c$ changes?

Calculation:

Consider the given function, $f\left(x\right)=\sqrt{1+c{x}^2}$ for different values of $c=-2,-1,0,1,2$ the graph is as shown,

  

Well graph observation shows that for positive values of $c$ graph increases from the point $\left(0,1\right)$ with minimum point as $1$

For negative values of $c$ the curve has maximum point $1$ as $c$ decreases, the minimum point becomes maximum point.

When $c=0$ the curve become horizontal line at the point $\left(0,1\right)$ .

Hence, the graph changes with $c$ .