Question 28

The graph of f(x + 2) is correctly represented by option E.

The transformation f(x + 2) indicates a horizontal shift of the graph of f(x) to the left by 2 units. This means that every point on the original graph of f(x) will be moved 2 units to the left, which is reflected accurately in option E.

A) lcagair-q49opa.png

This option does not represent the correct transformation since it shows a shift in the opposite direction or does not exhibit the necessary leftward shift of the entire graph. Therefore, it cannot be the graph of f(x + 2).

B) lcagair-q49opb.png

Similar to option A, this graph fails to demonstrate the leftward shift required for f(x + 2). Instead, it appears to show a vertical transformation or does not match the characteristics of the original graph.

C) lcagair-q49opc.png

This option also does not illustrate the required horizontal transformation. Instead, it seems to be a misrepresentation of the graph, as it does not reflect the left shift of 2 units.

D) lcagair-q49opd.png

This option does not depict the correct graph either, as it shows a shift that is inconsistent with the leftward movement of the original graph f(x). It fails to accurately represent f(x + 2).

E) lcagair-q49ope.png

This option correctly shows the graph of f(x) shifted left by 2 units, aligning perfectly with the transformation indicated by f(x + 2). It accurately represents the changes expected from the transformation.

Conclusion

Option E is definitively the correct answer because it accurately reflects the leftward shift of the graph by 2 units, as required by the transformation f(x + 2). All other options fail to demonstrate this necessary transformation, making them incorrect representations of the graph.