/*! 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 91 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 91

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. No quadratic functions have a range of \((-\infty, \infty)\)

Short Answer

Expert verified
The statement 'No quadratic functions have a range of \((-\infty, \infty)\)' is true.

Step by step solution

01

Understanding the Quadratic Function's Behavior

Given a quadratic function in the form \(f(x) = ax^2 + bx + c\), if the coefficient \(a\) is positive, then the graph opens upwards. Meaning, it has a minimum point (vertex) and hence the range is \([k, \infty)\) where \(k\) is the y-coordinate of the vertex. If the coefficient \(a\) is negative, then the graph opens downwards. Thus, it has a maximum point (vertex), and the range is \((-\infty, k]\) where \(k\) is the y-coordinate of the vertex.
02

Determining the Statement's Validity

From the previous understanding, it's clear that no quadratic function has a range of \((-\infty, \infty)\) since all quadratic functions have either a maximum or a minimum point hence the range can't extend infinitely in both directions. Consequently, the given statement is true.

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

Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}+1}{x}$$

Use a graphing utility to graph \(y-\frac{1}{x^{2}}, y-\frac{1}{x^{4}},\) and \(y-\frac{1}{x^{6}}\) in the same viewing rectangle. For even values of \(n,\) how does changing \(n\) affect the graph of \(y-\frac{1}{x^{n}} ?\)

You have 200 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? GRAPH CANNOT COPY.

This will help you prepare for the material covered in the next section. $$\text { Solve: } x^{3}+x^{2}-4 x+4$$

What is a polynomial incquality?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.