91Ó°ÊÓ

When we talk about evaluating functions, we mean finding the value of the function for specific values of its variable(s). For the polynomial function given in the problem, we need to evaluate it at two specific points: \(x = -1\) and \(x = 2\).

This involves substituting these values into the function and simplifying the resulting expression. Evaluating a function is a common problem in algebra and is a fundamental skill that will help you in many areas of math.

The key steps are:

• Recognizing the function you are given.
• Substituting the given value into the function.
• Carefully simplifying the expression to find the result.

By mastering these steps, you can evaluate any function confidently.

The substitution method is a straightforward technique used to evaluate functions. Here’s how it works:

Take the function and replace every instance of the variable with the given number. This helps us transform the function into a simpler arithmetic problem, which can then be easily solved.

In our example: \(f(x) = 6x - 4\), to find \(f(-1)\), you replace \(x\) with \( -1\):
\[f(-1) = 6(-1) - 4\]. -1 is substituted in place of x.
The same method applies when finding \(f(2)\). Simply substitute \(x\) with 2:
\[f(2) = 6(2) - 4\].

Practicing substitution helps you understand how inputs and outputs in functions relate. Remember, verify step-by-step calculations to avoid mistakes.

Polynomial calculation involves performing arithmetic operations on polynomials. For our example, the polynomial is linear (degree 1): \(f(x) = 6x - 4\).

To evaluate:

• First substitute the x value.
• Then, perform the multiplication and any arithmetic operations.

Here’s the detailed calculation for each part of the problem:

For \(f(-1)\):
\[ f(-1) = 6(-1) - 4 \]
Multiply: \[6 \times -1 = -6\]
Subtract: \[-6 - 4 = -10\]

For \(f(2)\):
\[ f(2) = 6(2) - 4 \]
Multiply: \[6 \times 2 =12\]
Subtract: \[12 - 4 = 8\]

Understanding each step in polynomial calculations is essential. Always start by performing the operations inside the parentheses and follow the arithmetic order correctly.