Question

the graph of g is a translation 2 units left of the graph of f. identify the graph of each function.

Explanation:

Step1: Recall translation rule

For a function \(y = f(x)\), a translation \(a\) units to the left gives \(y=f(x + a)\). Here \(a = 2\), so \(g(x)=f(x + 2)\). The graph of \(g\) will have the same shape as the graph of \(f\), but the key - points of \(g\) will be 2 units to the left of the corresponding key - points of \(f\).

Step2: Analyze graphs

Look for a pair of graphs where the second graph (graph of \(g\)) is the first graph (graph of \(f\)) shifted 2 units to the left. In the correct pair, if we take a point \((x,y)\) on the graph of \(f\), the corresponding point on the graph of \(g\) will be \((x-2,y)\).

Answer:

The correct pair of graphs is the one where the graph labeled \(g\) is the graph labeled \(f\) shifted 2 units to the left. Without specific labels on the given options in the image, we can't point out the exact choice, but the general rule is that the graph of \(g\) has all its features (such as vertex, intercepts etc.) 2 units to the left of the graph of \(f\).