Question

3 here is a graph of f and a graph of g. express g(x) in terms of f(x) using function notation. show your work here o g(x)=f(x)-3 o g(x)=f(x) o g(x)=f(x - 3) o g(x)=f(x + 3)

Explanation:

Step1: Analyze function - graph transformation

When we have a transformation of the form $y = f(x - h)$ for a function $y = f(x)$, it represents a horizontal shift. If $h>0$, the graph of $y = f(x)$ shifts to the right by $h$ units, and if $h < 0$, the graph shifts to the left by $|h|$ units. When we have $y=f(x)+k$, it represents a vertical shift. If $k>0$, the graph shifts up by $k$ units, and if $k < 0$, the graph shifts down by $|k|$ units.

Step2: Observe the graph

By looking at the graphs of $y = f(x)$ and $y = g(x)$, we can see that the graph of $g(x)$ is the graph of $f(x)$ shifted 3 units to the right.
For a function $y = f(x)$ shifted $h$ units to the right, the new - function is $y = f(x - h)$. Here $h = 3$, so $g(x)=f(x - 3)$.

Answer:

$g(x)=f(x - 3)$