for adults - 2

[logistic_guy]

Graph the function and its parent function. Then describe the transformation.

\(\displaystyle g(x) = x + 4\)

 

[Agent Smith]

Parent function [imath]f(x) = x[/imath]. Straight line, slope = [imath]1[/imath].

[imath]g(x) = f(x) + 4[/imath]. f shifted leftward by [imath]4[/imath]

 

[logistic_guy]

[imath]g(x) = f(x) + 4[/imath]. f shifted leftward by [imath]4[/imath]

What you did was shifting the parent function up by \(\displaystyle 4\).

Shifting the parent function to the left by \(\displaystyle 4\) is done like this:

\(\displaystyle f(x) = x\)

\(\displaystyle g(x) = f(x + 4) = x + 4\)

While \(\displaystyle f(x) + 4 = f(x + 4)\) for linear functions, we have to be precise what transformation we applied!

 

[logistic_guy]

Graph the function and its parent function. Then describe the transformation.

\(\displaystyle g(x) = x + 4\)

This is the graph of the function \(\displaystyle \textcolor{darkorange}{g(x) = f(x + 4) = x + 4}\) and its parent function \(\displaystyle \textcolor{blue}{f(x) = x}\).



\(\displaystyle \textcolor{red}{\bold{Transformation}}\): The graph of \(\displaystyle \textcolor{darkorange}{g(x)}\) is the result of shifting the graph of \(\displaystyle \textcolor{blue}{f(x)}\) \(\displaystyle 4\) units to the left.