Chapter 1.1, Problem 6E

To determine

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

Answer to Problem 6E

  $f$ belongs to the family of constant functions.

Explanation of Solution

Given information: Graph of function $f(x)=3$ .

As the graph is a flat straight line, $f$ belongs to the family of constant functions.

Graph of parent constant function is like:

  

Comparing given function with parent function $g(x)=1$ ,

the graph of given function exhibits vertical translation of $2units$ up w.r.t to parent function, The domain of both the function is all real numbers, range of given function is $y=3$ while that of the parent function is $y=1$ .