How to Evaluate a Cubic Function | Summary and Q&A

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June 7, 2023
by
The Math Sorcerer
How to Evaluate a Cubic Function

TL;DR

This video provides step-by-step instructions on how to evaluate a cubic function using specific values.

Key Insights

• ☺️ Evaluating a cubic function involves substituting specific x-values into the function equation.
• 🪈 The order of operations, including parentheses and exponentiation, is crucial when calculating the values.
• ❣️ The evaluations for different values of x can result in various y-values, revealing the behavior of the cubic function.
• 🦻 Evaluating functions helps understand how the function behaves for different inputs, aiding in further analysis and problem-solving.
• #️⃣ The given cubic function is a polynomial equation with a degree of 3, and its evaluations produce real number outputs.
• ☺️ The process of evaluating a cubic function can be extended to any given x-value using the same principles shown in the video.
• 👻 Evaluating functions is an essential skill in mathematics, as it allows for the understanding and analysis of various mathematical problems.

Transcript

in this video we're going to do an example of evaluating a cubic function our function is f of x equals X cubed minus 2x squared plus 2X minus 4. and the question is to find F of 0 F of 1 f of negative 1 and F of 2. let's carefully work through this solution let's start with f of zero so F of 0 means we want to evaluate our function f at the x valu... Read More

Questions & Answers

Q: How do you evaluate f(0) for the given cubic function?

To evaluate f(0), substitute 0 for x in the function. This results in f(0) = 0^3 - 2(0^2) + 2(0) - 4, which simplifies to -4.

Q: What is the value of f(1) for the cubic function?

By replacing x with 1 in the function, we get f(1) = 1^3 - 2(1^2) + 2(1) - 4. Simplifying further, f(1) equals -3.

Q: How can f(-1) be evaluated using the given cubic function?

Replace each x in the function with -1, considering the negative sign carefully. This yields f(-1) = (-1)^3 - 2(-1)^2 + 2(-1) - 4. Simplifying, we find that f(-1) equals -9.

Q: What is the value of f(2) for the cubic function provided?

Substituting 2 for x in the function gives f(2) = 2^3 - 2(2^2) + 2(2) - 4, which simplifies to 0.

Summary & Key Takeaways

• The video demonstrates how to evaluate a cubic function, f(x) = x^3 - 2x^2 + 2x - 4, for the values f(0), f(1), f(-1), and f(2).

• By substituting the given x values into the cubic function, the corresponding y-values are calculated.

• The evaluations for f(0), f(1), f(-1), and f(2) are -4, -3, -9, and 0, respectively.

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