intercept of a given function, f(x) = e^(2x^2interintercept of a given function, f(x) = e^(2x^2 - x).cept of a given function, f(x) = e^(2x^2 - x). - x).

To find the y-intercept of a given function, \( f(x) \), you need to evaluate the function at \( x = 0 \). The y-intercept is the point where the graph of the function crosses the y-axis.

Given the function:

\[
f(x) = e^{(2x^2 - x)}
\]

Substitute \( x = 0 \) into the function:

\[
f(0) = e^{(2(0)^2 - 0)} = e^{(0)} = e^0 = 1
\]

So, the y-intercept of the function \( f(x) = e^{(2x^2 - x)} \) is \( (0, 1) \).

Would you like to dive deeper into any other aspect of this problem?

Here are 5 related questions:
1. How do you find the x-intercepts of the function \( f(x) = e^{(2x^2 - x)} \)?
2. What is the general process for finding intercepts of exponential functions?
3. How does the derivative of \( f(x) = e^{(2x^2 - x)} \) behave?
4. Can you sketch the graph of \( f(x) = e^{(2x^2 - x)} \)?
5. What is the significance of intercepts in analyzing the behavior of functions?

**Tip:** When working with exponential functions, remember that the function never crosses the x-axis unless the exponent is negative infinity.

Learn how to find the y-intercept of the function f(x) = e^(2x^2 - x) with a detailed step-by-step solution. This problem covers exponential functions and function evaluation at a specific point. Suitable for students in Grades 10-12.

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