/*! 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 15 Evaluate the given functions. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 15

Evaluate the given functions. $$f(x)=6 ; \text { find } f(-2) \text { and } f(0.4)$$.

Short Answer

Expert verified
Both \( f(-2) \) and \( f(0.4) \) are equal to 6.

Step by step solution

01

Understand the Given Function

The function given is a constant function, where for every value of \( x \), the function \( f(x) \) returns the constant value 6. This means that the value of the function does not change regardless of the input.
02

Substitute \( x = -2 \) into the Function

Since \( f(x) = 6 \) is a constant function, substituting \( x = -2 \) will result in the function evaluating to the same constant value. Thus, \( f(-2) = 6 \).
03

Substitute \( x = 0.4 \) into the Function

Similarly, since the function is constant, substituting \( x = 0.4 \) will still yield the constant value of the function. Hence, \( f(0.4) = 6 \).

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.

Function Evaluation
Evaluating a function is a fundamental concept in mathematics. It involves determining the output of a function for a given input. Consider the function in our problem: \( f(x) = 6 \). This exemplifies a constant function, where the function produces the same result regardless of the input value for \( x \).
To evaluate \( f(-2) \), we substitute \(-2\) in place of \( x \) in the function. Since our function is constant, we can immediately state that \( f(-2) = 6 \).
  • The substitution simply confirms the value of the function, ensuring that the operation is rigorous, even if no calculation seems necessary.
  • Similarly, evaluating \( f(0.4) \) involves substituting \( 0.4 \) in place of \( x \) again reinforcing that \( f(0.4) = 6 \).
By evaluating a function, we exercise the application of function rules, highlighting whether a function varies or remains unchanged with input.
Independent Variable
In the realm of functions, the concept of the independent variable is crucial. The independent variable represents the input that you give to a function. In our case with \( f(x) = 6 \), \( x \) serves as the independent variable.
What this means is for every different value we assign to \( x \), the function should calculate an output. However, in a constant function, the situation is unique:
  • No matter what value \( x \) might take, the outcome remains identical.
  • The independent variable highlights that while inputs may vary, the constant function does not rely on \( x \) to determine its value.
This feature makes constant functions straightforward yet powerful in illustrating how a function primarily conditioned by its definition can forgo dependence on different inputs.
Constant Value
The constant value in a function signifies that the output remains unchanged regardless of the input. For the function \( f(x) = 6 \), the constant value is 6. Such functions are called constant functions because their behavior is defined purely by this unchanging outcome.
Understanding constant values is simple:
  • For any \( x \), the function evaluates to 6, underscoring its predictable nature.
  • Constant functions are horizontal lines when graphed on a coordinate plane, depicting the unwavering output across all \( x \)-values.
  • The constant value makes calculations quicker, as no computation is needed to arrive at the result 鈥� substituting any \( x \) directly gives the constant value.
Constant functions are a perfect example of consistency and simplicity in mathematical operations, often used in scenarios where fixed conditions are modeled.

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

A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator. $$y=\sqrt{2 x+1}, \text { up } 1, \text { left } 1$$

A function and how it is to be shifted is given. Find the shifted function, and then display the given function and the shifted function on the same screen of a graphing calculator. $$y=\frac{2}{x}, \text { left } 4$$

Graph the given functions. $$y=\sqrt{x^{2}-16}$$

Graph the indicated functions. Plot the graphs of (a) \(y=x^{2}-x+1\) and (b) \(y=\frac{x^{3}+1}{x+1}\) Explain the difference between the graphs.

Solve the given problems. A balloon is being blown up at a constant rate. (a) Sketch a reasonable graph of the radius of the balloon as a function of time. (b) Compare to a typical situation that can be described by \(r=\sqrt[3]{3 t}\) where \(r\) is the radius (in \(\mathrm{cm}\) ) and \(t\) is the time (in s).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics 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.