Chapter 3.5, Problem 64PFA

a

To determine

To describe: The transformation of graph of g(x) from the graph of $f(x)=x$ .

Explanation of Solution

Given information: The graph of $g(x)=ax+k$ as a transformation of $f(x)=x$ .

Since

  $\begin{array}{l}f(x)=x\\ f(x+k)=x+k\end{array}$

Now the line changes on vertical axis that is upwards or downwards depending on the value of k .

  $\begin{array}{l}f(x+k)=f(x)+k\\ f(ax+k)=af(x)+\text{k}\end{array}$

In this step line changes horizontally as well due to value of a which magnifies x

  $\text{Therefore},g(x)=f(ax+k)$

Which describes the transformation across g(x).

b

To determine

To find: The value of $k$ from the graph of.

Answer to Problem 64PFA

The value of $k$ is $-6$ .

Explanation of Solution

Given information: The graph of $g(x)=ax+k$ .

From the graph we can say that when the value of x-coordinate is 0 then the value of y-coordinate comes to $-6$ put this points on the $g(x)=ax+k$ we get $k=-6$ .

c

To determine

To write : The value of $a$ from the graph of $g(x)=ax+k$ which is a transformation of the graph of $f(x)=x$ .

Answer to Problem 64PFA

The value of $a$ is $2$ .

Explanation of Solution

Given information: The graph of $g(x)=ax+k$ .

From the graph we can say that when the value of y-coordinate is 0 then the value of x-coordinate comes to $3$ put this points on the $g(x)=ax+k$ we get $a=2$ .

d

To determine

To Write: The equation of $g(x)$ .

Answer to Problem 64PFA

The equation is $g(x)=2x-6$ .

Explanation of Solution

Given information: The graph of $g(x)=ax+k$ .

From the graph and the above results we can conclude that the equation of the transformation graph is $g(x)=2x-6$ .