To evaluate the function \( f(x) = 2x^3 + 4 \) at \( x = -3 \), we substitute \(-3\) for \(x\) in the function:

\[
f(-3) = 2(-3)^3 + 4
\]

Now, calculate \((-3)^3\):

\[
(-3)^3 = -27
\]

Then, multiply \(-27\) by \(2\):

\[
2 \times (-27) = -54
\]

Finally, add \(4\) to \(-54\):

\[
-54 + 4 = -50
\]

Thus, the value of the function \( f(-3) \) is \(-50\).

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you find the derivative of \( f(x) = 2x^3 + 4 \)?
2. What is the general process for evaluating polynomial functions?
3. How does changing the coefficient in a cubic function affect its graph?
4. What are the roots of the function \( f(x) = 2x^3 + 4 \)?
5. How do transformations affect the graph of cubic functions?
6. What is the difference between evaluating a function and solving an equation?
7. How do you graph a cubic function like \( f(x) = 2x^3 + 4 \)?
8. How does the leading coefficient affect the end behavior of a polynomial function?

**Tip:** When evaluating functions, always perform operations inside the parentheses first, then follow the order of operations.

Learn how to evaluate the function f(x) = 2x^3 + 4 at x = -3 with a detailed step-by-step solution. This problem involves polynomial evaluation and order of operations, suitable for students in Grades 9-12.

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