/*! 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 68 Graph the function and determine... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 68

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$ f(x)=4 x+2 $$

Short Answer

Expert verified
The function \(f(x) = 4x + 2\) is greater than or equal to zero for all \(x\) in the interval \([-1/2, \infty)\.

Step by step solution

01

Graph the function

The function \(f(x) = 4x + 2\) is a linear function with a slope of 4 and a y-intercept of 2. The graph of the function is a straight line which passes through the y-axis at point (0,2) and inclined to x-axis at angle whose tangent is 4
02

Find the function's zero

The zero of the function 鈥� the value of \(x\) for which \(f(x) = 0\) 鈥� can be calculated by setting \(4x + 2 = 0\). Solving for \(x\), we get \(x = -1/2\).
03

Determine intervals

Since this is a linear function without any breaks or oscillation, it is either greater than or equal to zero, or less than zero. As we found that the zero of the function is at \(x = -1/2\), we need to check any point to the left of -1/2, and any point to the right of -1/2. For instance, at \(x = -1\) (to the left of -1/2), \(f(x) = 4(-1) + 2 = -2 < 0\). At \(x = 0\) (to the right of -1/2), \(f(x) = 4*(0) + 2 = 2 > 0\). Thus the function \(f(x) \geq 0\) for \(x \geq -1/2\).

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!

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

Determine whether the function has an inverse function. If it does, find the inverse function. $$ p(x)=-4 $$

Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=20 $$

Determine whether the variation model is of the form \(y=k x\) or \(y=k / x,\) and find \(k .\) Then write \(a\) model that relates \(y\) and \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & 24 & 12 & 8 & 6 & \frac{24}{5} \\ \hline \end{array} $$

Consider the functions given by \(f(x)=x+2\) and \(f^{-1}(x)=x-2 .\) Evaluate \(f\left(f^{-1}(x)\right)\) and \(f^{-1}(f(x))\) for the indicated values of \(x .\) What can you conclude about the functions? $$ \begin{array}{|l|l|l|l|l|} \hline x & -10 & 0 & 7 & 45 \\ \hline f\left(f^{-1}(x)\right) & & & & \\ \hline f^{-1}(f(x)) & & & & \\ \hline \end{array} $$

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{x-2} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.