Chapter 1, Problem 10CT

To determine

To match: The transformation of $f(x)$ with its graph, the write a rule for $g$ .

Answer to Problem 10CT

  $g$ matches $C$ and the rule for $g$ is $g(x)=3x-2$ .

Explanation of Solution

Given information: Functions are $f(x)=x$ and $g(x)=3f(x)-2$ , a graph is also given.

Graph:

  

Red line represents initial function, blue represents intermediate function and green represents final transformed function.

Interpretation:

To obtain $g(x)=3f(x)-2$ , first $f$ has to be stretched vertically by a factor of $3$ , such that intermediate function is $h(x)=3f(x)$ , then translated $2$ units down .

Thus, $g$ matches $C$ and the rule for $g$ is $g(x)=3x-2$ .