Evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x² +1 b. h (-1)

Verified step by step guidance

1. Step 1: Start by substituting the given value of the independent variable, x = -1, into the function h(x). The function is h(x) = x⁴ - x² + 1. Replace every occurrence of x with -1.
2. Step 2: Write the substituted expression: h(-1) = (-1)⁴ - (-1)² + 1.
3. Step 3: Simplify each term in the expression. Recall that (-1)⁴ means multiplying -1 by itself four times, and (-1)² means multiplying -1 by itself two times.
4. Step 4: Combine the simplified terms to get the final expression for h(-1).
5. Step 5: Verify that all calculations are simplified correctly and ensure the expression is fully reduced.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, we replace 'x' in the function h(x) = x^4 - x² + 1 with -1. This process allows us to compute the output of the function for that particular input.

Polynomial Functions

A polynomial function is a mathematical expression that involves variables raised to whole number powers, combined using addition, subtraction, and multiplication. The function h(x) = x^4 - x² + 1 is a polynomial of degree 4, which indicates the highest power of x present in the expression. Understanding polynomial functions is essential for evaluating and simplifying them.

Simplification of Expressions

Simplification of expressions involves reducing a mathematical expression to its simplest form. After evaluating the function h(-1), we will combine like terms and perform arithmetic operations to arrive at a single numerical value. This step is crucial for providing a clear and concise answer to the evaluation of the function.