Chapter 4.3, Problem 82E

a.

To determine

To define: to draw the graphs of the functions of family for c=1,2,3,4 , $f\left(x\right)=c\log x$ .

Answer to Problem 82E

The points of the graph x is 1 then y is 0 , if x is 2 then y is $c\log 2$ ,if x is 3 then y is $c\log 3$ .

  

Explanation of Solution

Given information:

The function to draw the graphs family of c=1,2,3,4 , $f\left(x\right)=c\log x$ .

The function todraw the graphs of the family of c=1,2,3,4 , $f\left(x\right)=c\log x$ .

As take x=1,

  $\begin{array}{c}y=c\log \left(1\right)=0\\ x=2\\ y=c\log \left(2\right)\end{array}$

Now for x=3:

  $y=c\log \left(3\right)$ ,

The log function can be graphed using the vertical asymptote at x=0 , and the points $\left(1,c\log \left(1\right)\right),\left(2,c\log 2\right),\left(3,c\log 3\right)$ .

The graph of the given equation:

  

b.

To determine

To define: relation of graph part ‘a’ of the function $f\left(x\right)=c\log \left(x\right)$ .

Answer to Problem 82E

The graph of part ‘a’ of the give function $f\left(x\right)=\log \left(cx\right)$ is related.

  

The graph of the function $f\left(x\right)=c\log \left(x\right)$ is th graph of $f\left(x\right)=\log \left(x\right)$ shifted upward log c units.

Explanation of Solution

Relation of graph part ‘a’ of the function $f\left(x\right)=c\log \left(x\right)$ .

Given information:

Relation of graph part ‘a’ of the function $f\left(x\right)=c\log \left(x\right)$

The graph of part ‘a’ of the give function $f\left(x\right)=c\log \left(x\right)$ .

  

The graph of the function $f\left(x\right)=c\log \left(x\right)$ is th graph of $f\left(x\right)=\log \left(x\right)$ shifted upward log c units.

The values of the function for every x,y, as x increases then y also increases.

The solution of the give equation