/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Express the function (or rule) i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 9

Express the function (or rule) in words. $$h(x)=x^{2}+2$$

Short Answer

Expert verified
Square the input, then add 2.

Step by step solution

01

Understand the Function

The function given is represented as \( h(x) = x^2 + 2 \). In this expression, \( h(x) \) indicates the output of the function when \( x \) is the input.
02

Break Down the Expression

The function can be dissected into two parts: \( x^2 \) and \(+2 \). Here, \( x^2 \) implies squaring the input \( x \), and \(+ 2 \) denotes that we add 2 to the result of \( x^2 \).
03

Describe the Function in Words

In words, the function \( h(x) = x^2 + 2 \) can be expressed as: "Square the input \( x \), then add 2 to the result."

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Squaring a Number
Squaring a number means multiplying that number by itself. When you square a number, the result is called a 'square'. For example, if the number is 3, squaring it would involve calculating \(3 \times 3\), which equals 9. Squaring is often represented with an exponent of 2, as in \(x^2\), where \(x\) is any number.

The process of squaring a number is straightforward:
  • Choose a number (this will be your base).
  • Multiply the number by itself.
  • The product is the square of the number.

Squaring can only ever give you a number greater than or equal to zero. This is because a negative number times itself still results in a positive product. So, when you come across \(x^2\) in mathematics, always remember it's the input number multiplied by itself, guaranteeing a non-negative result.
Addition in Mathematics
Addition is one of the basic arithmetic operations that involves finding the sum of two or more numbers. It's represented by the plus symbol \(+\). When you add numbers together, you combine their values to reach a total. For instance, if you add 4 and 2, the result is 6, because these numbers together count up to 6.

Let's see how addition works with simple steps:
  • Identify the numbers you wish to add (addends).
  • Combine their values by adding them together.
  • The resulting number is called the sum.

In the context of the function \(h(x) = x^2 + 2\), you're adding the constant 2 to the squared result of the input \(x\). This is a straightforward addition operation but is crucial in changing the output of the function compared to just squaring \(x\) alone.
Exploring Input-Output Relationships
The concept of input-output relationships is fundamental in understanding functions in mathematics. Simply put, a function takes an 'input', performs some operation on it, and produces an 'output'. This is often written in function notation, like \(h(x)\), where \(x\) is the input.

Think of it like a machine:
  • You input a number into the function.
  • The function processes this number according to its own rules or formula.
  • The function then outputs a result.

In our specific example \(h(x) = x^2 + 2\), you input a value for \(x\). The function first squares this value, and then adds 2 to the squared result to give the output. Each input \(x\) will yield a unique output, depending on what the operation requires. This predictable relationship allows us to use functions to model real-world situations and solve problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Finance An investor has \(\$ 100,000\) to invest in three types of bonds: short- term, intermediate-term, and long-term. How much should she invest in each type to satisfy the given conditions? Short-term bonds pay \(4 \%\) annually, intermediate-term bonds pay \(6 \%,\) and long-term bonds pay \(8 \% .\) The investor wishes to have a total annual return of \(\$ 6700\) on her investment, with equal amounts invested in intermediate- and long-term bonds.

Suppose you have to solve a linear system with five equations and five variables without the assistance of a calculator or computer. Which method would you prefer: Cramer's Rule or Gaussian elimination? Write a short paragraph explaining the reasons for your answer.

Find the inverse of the matrix. $$\begin{aligned} &\left[\begin{array}{rr} a & -a \\ a & a \end{array}\right]\\\ &(a \neq 0) \end{aligned}$$

Let \(A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right] .\) Calculate \(A^{2}, A^{3}\) \(A^{4}, \ldots\) until you detect a pattern. Write a general formula for \(A^{n}\)

Evaluate the minor and cofactor using the matrix \(A\) $$A=\left[\begin{array}{rrr} 1 & 0 & \frac{1}{2} \\ -3 & 5 & 2 \\ 0 & 0 & 4 \end{array}\right]$$ $$M_{23}, A_{23}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.