If f(x) is given by the following graph, then which graph is f(|x|)?A.B.C.D.E.SUBMITarrow_backPREVIOUS

In order to determine which graph corresponds to $f(|x|)$, we can follow these steps:

1. Break Down the Problem

• We need to understand how the transformation $f(|x|)$ affects the original function $f(x)$.
• Specifically, $f(|x|)$ means that for every negative $x$, the function will reflect the positive $x$ values onto the left side.

2. Relevant Concepts

• The operation $|x|$ compresses negative inputs to their positive counterparts.
• For any $x < 0$, $f(|x|) = f(-x)$.
• Thus, the behavior of the graph for $x < 0$ should mirror the behavior of the graph for $x > 0$.

3. Analysis and Detail

1. Examine the graph of $f(x)$ for positive $x$.
2. Reflect this portion of the graph across the y-axis to account for $f(|x|)$.
3. Leave the part of the graph for positive $x$ unchanged.

4. Verify and Summarize

• After reflecting the right-side graph (for positive $x$) into the left side (for negative $x$), compare the resulting graph with the provided options (A, B, C, D, E).
• The correct graph will have both the original graph in the positive x-region and a mirror image in the negative x-region.

Final Answer

The correct graph for $f(|x|)$ is the one that shows the reflection of the positive x values to the negative side. Choose the option that exhibits this symmetric property.