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is this under the topics of functions or what

Yes, this problem falls under the topic of **functions**. Specifically, it deals with sketching the graph of a rational function:

\[
y = \frac{1}{1 + x} + 1
\]

In problems like this, you'll typically need to:

1. Identify **intercepts**: Find where the function crosses the x-axis and y-axis.
2. Determine **asymptotes**: Look for vertical and horizontal asymptotes that represent values where the function approaches infinity or a fixed number.
3. Analyze the **behavior of the function**: Consider how the function behaves as \( x \to \infty \) or \( x \to -\infty \), and at critical points where the denominator could lead to undefined values.

These topics belong to the study of functions, particularly rational functions, which include operations involving fractions with polynomials.

Would you like me to help solve and sketch this function, or would you prefer more details on intercepts and asymptotes?

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Here are 5 related questions to deepen your understanding:
1. How do you find vertical asymptotes for rational functions?
2. What are the steps to determine the horizontal asymptote of a function like this one?
3. How would you calculate the x-intercept of the function \( y = \frac{1}{1 + x} + 1 \)?
4. What is the general behavior of rational functions at extreme values of \( x \)?
5. How does shifting a rational function (like adding \( +1 \)) affect its graph?

**Tip**: Always check the denominator for values that make it zero—this usually indicates vertical asymptotes.

Sketch the graph of y = 1/(1 + x) + 1, showing all intercepts and asymptotes.

Learn how to sketch the rational function y = 1/(1 + x) + 1 by finding its intercepts and asymptotes. This tutorial covers the steps to identify the vertical asymptote at x = -1 and the horizontal asymptote at y = 1, with a detailed graph.

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