The graph of the function y = f(x) is shown in the xy -plane above. Which of the following is the graph of f(x + 2) ?
The graph of f(x + 2) is represented by option E.
The transformation f(x + 2) indicates a horizontal shift of the graph f(x) to the left by 2 units. This means that every point on the original graph will move leftward, resulting in the corresponding new graph that maintains the same shape but has its features relocated.
This graph does not represent a leftward shift of the original graph. Instead, it appears to be a reflection or distortion of the original function, which does not accurately depict the transformation required for f(x + 2).
This option suggests a rightward shift of the graph, which contradicts the transformation indicated by f(x + 2). A rightward shift would be represented by f(x - 2), making this option incorrect.
The graph in this option does not show the correct leftward shift. Instead, it appears to be a vertical shift or alteration in shape, which does not correspond to the transformation of f(x + 2).
This graph does not match the expected outcome of applying the transformation f(x + 2). It seems to modify the original function in a way that does not reflect a simple horizontal shift, thus making it incorrect.
This option accurately reflects the leftward shift of the graph by 2 units. All points from the original graph f(x) have moved left, maintaining the shape and characteristics of the function.
The transformation f(x + 2) necessitates a horizontal shift of the graph to the left by 2 units. Among the given choices, only option E correctly represents this transformation. The other options exhibit various inaccuracies, such as reflections, distortions, or incorrect shifts, thereby confirming option E as the only valid representation of the function's transformation.
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