Chapter 1.2, Problem 1Q

To determine

To identify: The function family to which $g$ belongs and then to compare the graph of the function to the graph of its parent function.

Answer to Problem 1Q

Parent function is $f(x)=x$ , $g$ is horizontally stretched by a factor of $3$ and translated vertically $1$ unit down.

Explanation of Solution

Given information: Function is $g(x)=\frac{1}{3}x-1$ .

Calculation:

  $g$ belongs to family of linear functions,

Parent function is $f(x)=x$ .

  

Red line represents the given function whereas blue line represents parent function.

Given function is horizontally stretched by a factor of $3$ and translated vertically $1$ unit down with respect to the parent function.

Domain of parent function: All real numbers

Range of parent function: All real numbers

Domain of given function: All real numbers

Range of given function: All real numbers

Thus, parent function is $f(x)=x$ , $g$ is horizontally stretched by a factor of $3$ and translated vertically $1$ unit down .