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

$y=f(x-2)$

Short answer

For function $y=f\left(x\right)-2$ , the graph function f is shifted downwards bylocalid="1646043418087" $2$units whereas, for the function $y=f(x-2)$, the graph of the function f is shifted to the right by $2$units.

Step-by-step solution

Step 1. Given Information 

The given function is given asf.

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.