Chapter 1.2, Problem 8Q

To determine

To graph: The function and its parent function and then to describe the transformation.

Answer to Problem 8Q

Parent function is $g(x)=x^2$ , $f$ is vertically shrunk by a factor of $\frac{1}{4}$ and translated vertically $1$ unit up with respect to the parent function.

Explanation of Solution

Given information: Function is $f(x)=\frac{1}{4}{x}^2+1$ .

Graph:

  $f$ belongs to the family of quadratic functions,

Parent function is $g(x)=x^2$ .

  

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

Interpretation:

  $f$ is vertically shrunk by a factor of $\frac{1}{4}$ and translated vertically $1$ unit up with respect to the parent function.

Thus, parent function is $g(x)=x^2$ , $f$ is vertically shrunk by a factor of $\frac{1}{4}$ and translated vertically $1$ unit up with respect to the parent function.