Q. 95 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that the graph of a function f  is known. Explain how the graph of $y=f\left(x\right)-2$ differs from the graph of

$y=f(x-2)$

Step-by-Step Solution

Answer

 For function $y=f\left(x\right)-2$ , the graph function f  is shifted downwards by $2$units whereas, for the function $y=f(x-2)$, the graph of the function f  is shifted to the right by $2$ units.

Step 1. Given Information

The given function is given as f. 

Step 2. Difference between the graphs

$y=f\left(x\right)-k$We know that, for the function , the graph of the function f  is shifted downwards by k units and for the function $y=f(x-k)$ the graph of the function f  is shifted to the right by k units. 

Thus, for the function $y=f\left(x\right)-2$, the graph function f  is shifted downwards by $2$ units whereas, for the function $y=f(x-2)$, the graph of the function f  is shifted to the right by $2$ units.