Evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 a. h (3)

Verified step by step guidance

1. Step 1: Understand the problem. The function h(x) = x³ − x + 1 is given, and we are tasked with evaluating the function at x = 3. This means substituting x = 3 into the function and simplifying the resulting expression.
2. Step 2: Substitute x = 3 into the function h(x). This gives h(3) = (3)³ − (3) + 1.
3. Step 3: Simplify the first term, (3)³. Recall that raising a number to the power of 3 means multiplying the number by itself three times: (3)³ = 3 × 3 × 3.
4. Step 4: Simplify the remaining terms. After calculating (3)³, subtract 3 and then add 1 to the result.
5. Step 5: Combine all the simplified terms to find the value of h(3). This will give the final result of the function evaluation.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, to evaluate h(3), you replace x in the function h(x) = x³ − x + 1 with 3. This process allows you to find the output of the function for that particular input.

Polynomial Functions

The function h(x) = x³ − x + 1 is a polynomial function, which is a mathematical expression consisting of variables raised to whole number powers and coefficients. Understanding polynomial functions is essential as they can exhibit various behaviors, such as growth rates and turning points, depending on their degree and coefficients.

Simplification

Simplification in mathematics refers to the process of reducing an expression to its simplest form. After evaluating the function h(3), you may need to combine like terms or perform arithmetic operations to arrive at a final, simplified result. This step is crucial for clarity and ease of interpretation in mathematical expressions.