Evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 b. h (-2)

Verified step by step guidance

1. Step 1: Understand the problem. You are given a function h(x) = x³ − x + 1, and you need to evaluate this function at x = -2. This means substituting -2 for x in the function.
2. Step 2: Substitute -2 into the function h(x). Replace every occurrence of x in the equation h(x) = x³ − x + 1 with -2. The equation becomes h(-2) = (-2)³ − (-2) + 1.
3. Step 3: Simplify the first term (-2)³. Recall that raising a negative number to an odd power results in a negative value. Compute (-2)³ = -8.
4. Step 4: Simplify the second term −(-2). Remember that subtracting a negative number is equivalent to adding its positive counterpart. So, −(-2) = 2.
5. Step 5: Combine all terms. Add the results from the previous steps: -8 (from (-2)³), +2 (from −(-2)), and +1 (the constant term). Simplify the expression to find h(-2).

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, to evaluate h(-2), we replace x in the function h(x) = x³ − x + 1 with -2. This process allows us 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 increasing or decreasing trends, and can be evaluated at specific points to find their values.

Simplification

Simplification in mathematics refers to the process of reducing an expression to its simplest form. After evaluating the function h(-2), it is important to simplify the resulting expression to make it easier to interpret. This may involve combining like terms or performing arithmetic operations to arrive at a final, concise answer.