Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 32b

Chapter 3, Problem 32b

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

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.

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.

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.

Step 4: Simplify the second term −(-2). Remember that subtracting a negative number is equivalent to adding its positive counterpart. So, −(-2) = 2.

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).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

Guided course

04:15

Multiply Polynomials Using the Distributive Property

Related Practice

Textbook Question

Use the graph of y = f(x) to graph each function g. g(x) = 2f(x+2) − 1

1289

views

Textbook Question

Which graphs in Exercises 29–34 represent functions that have inverse functions?

630

views

Textbook Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−3, 6) and (3, −2)

132

views

Textbook Question

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

142

views

Textbook Question

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

views

Textbook Question

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

158

views