Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False 

To graph ${(x-2)}^3$, shift the graph of $y=x^3$ to the left $2$ units.

Step-by-Step Solution

Answer

The statement is false, since the graph ${(x-2)}^3$ should be graphed horizontally right to two unit.

Step 1. Given

The graph $y={(x-2)}^3$

By shifting $y=x^3$ to left to two units.

Step 2. Horizontal shift.

If the argument $x$ of a function $f$ is replaced by $x+h,h>0$, the graph of the new function $y=f(x+h)$ is the graph of $f$ shifted horizontally left $h$ units.

If the argument $x$ of a function $f$ is replaced by $x-h,h>0$ the graph of the new function $y=f(x-h)$ is the graph of $f$ shifted horizontally right  $h$ units.

Step 3. Compare ( x + h ) with ( x - 2 )

So the parent function is $y=x^3$

And the graph $y={(x-2)}^3$ is graphed by shifting horizontally the basic function right to two units.

So the given statement is false.