Question 27

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

The transformation f(x + 2) indicates a horizontal shift of the graph of f(x) to the left by 2 units. Therefore, the correct graph reflects this leftward movement.

A) 1756128741q13.png

This option does not represent the correct transformation. The graph appears to have been shifted in the opposite direction, which is not consistent with the transformation f(x + 2), as it should be shifted left, not right.

B) 1756128788q13.png

Similar to option A, this graph also shows an incorrect transformation. It seems to maintain the same position as f(x), indicating no shift, which does not align with the leftward shift required by f(x + 2).

C) 1756128837q13.png

This option also fails to demonstrate the required transformation. The graph in this option appears to have been shifted down or altered in some other way, rather than moving left by 2 units as necessitated by the transformation.

D) 1756128874q13.png

This is the correct option, as it accurately depicts the graph of f(x) shifted left by 2 units. The features of the graph, including peaks and intercepts, are appropriately adjusted to reflect this transformation.

E) 1756128920q13.png

This option does not represent the correct transformation. The graph appears to be shifted in a manner inconsistent with a leftward shift of 2 units, suggesting an incorrect application of the transformation.

Conclusion

The graph that accurately reflects the transformation f(x + 2) is option D, showcasing a leftward shift of the original graph by 2 units. All other options either exhibit no transformation or an incorrect shift, confirming that they do not satisfy the requirements of the given transformation.