Chapter 2.1, Problem 41E

To determine

To justify each step in writing a function g based on the transformation of $f\left(x\right)=2x^2+6x$ .

Answer to Problem 41E

Function g based on the transformation of $f\left(x\right)=2x^2+6x$ .

Explanation of Solution

Given Information: The function of $f\left(x\right)=2x^2+6x$ is translated 6 units down followed by a reflection in the x-axis.

Calculation:

  $h\left(x\right)=f\left(x\right)-6$

  $\text{The function }f\left(x\right)\text{ is translated 6 units down}$

  $=2x^2+6x-6$

  $\text{Substitute }f\left(x\right)=2x^2+6x$

  $g\left(x\right)=-h\left(x\right)$

  $g\left(x\right)\text{ represents the reflection of }h\left(x\right)\text{ on the }x\text{-axis}$

  $\text{=}-\left(2x^2+6x-6\right)$

  $\text{Substitute }h\left(x\right)=2x^2+6x-6$

  $\text{=}-2x^2-6x+6$

  $\text{Multiply the expression }2x^2+6x-6\text{ by}-1$