https://r2.erweima.ai/mathbot/image/1726826871183cx50rqe8.jpg

The graph of \( f(x) = \ln |x| \) is symmetric about the \( y \)-axis, confirming that the function is even. There is a vertical asymptote at \( x = 0 \), as the function is undefined there. For both positive and negative values of \( x \), the graph shows the logarithmic behavior but mirrored across the \( y \)-axis for negative \( x \).

Would you like further clarification or additional details?

Here are 5 related questions to deepen your understanding:
1. How can you define the domain of the function \( f(x) = \ln |x| \)?
2. What is the behavior of \( f(x) \) as \( x \) approaches 0 from the positive and negative sides?
3. How does the derivative of \( f(x) = \ln |x| \) behave for different \( x \) values?
4. What are the transformations involved in deriving \( \ln |x| \) from \( \ln x \)?
5. How does the graph of \( f(x) = \ln |x| \) differ from that of \( g(x) = | \ln x | \)?

**Tip:** When verifying if a function is even, always check the symmetry of its graph as well as its algebraic form!

Demuestre que f(x) = ln |x| es una función par y trace la gráfica.

Learn how to demonstrate that the logarithmic function f(x) = ln |x| is an even function through its properties and symmetry. A step-by-step guide includes a graph to visualize the behavior of the function. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation