Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q5. (page 597)

Considery=x2−7x+6. What are the domain and range?

Short Answer

Expert verified

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or {y/y≥−6.25}.

Step by step solution

01

Step 1. Define the concept.

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x-values that will make the function "work" and will output real y-values.

Therangeof a function is the complete set of all possibleresulting valuesof the dependent variable (y,usually) after we have substituted the domain.

02

Step 2. Graphical representation of the quadratic function.

Draw the graph of the function: y=x2−7x+6.

03

Step 3. State the domain and range of the function.

The function y=x2−7x+6has the domain as all real numbers. The range is all real numbers greater than or equal to the minimum value. Since the function has a minimum value at x=1.5. Therefore, the range is {y|y≥− 6 .25}.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Considery=x2−5x+4

Write the equation of the axis of symmetry.

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of a quadratic function has a maximum if the coefficient of the x2is positive.

Find the next three terms of each arithmetic sequence.

16,4,−8,−20,...

Write a formula that can be used to find the perimeter of a figure containing nsquares.

MULTIPLE REPRESENTATIONS in this problem, you will investigate solving quadratic equations using tables.

a. ALGEBRAIC Determine the related function for each equation. Copy and complete the table below.

b. GRAPHICAL Graph each related function with a graphing calculator.

c. ANALYTICAL use the table feature on your calculator to determine the zeros of each related function. Record the zeros in the table above. Also, record the values of the function one unit less than and one unit more than each zero.

d. VERBAL Compare the signs of the function values for x values just before and just after a zero. What happens to the sign of the function value before and after a zero?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.

Sign-up for free