/*! 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 19 Each equation defines y as a fun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 19

Each equation defines y as a function of \(x .\) Create a table that shows the values of the function for the given values of \(x\) $$y=x^{2}+x-4 ; \quad x=-2,-1.5,-1, \ldots, 3,3.5,4$$

Short Answer

Expert verified
Question: Create a table of values for the function \(y=x^2+x-4\) for the given set of x-values from -2 to 4 with a step of 0.5. Answer: | x | y | |-------|--------| | -2 | -2 | | -1.5 | -3.25 | | -1 | -4 | | -0.5 | -3.75 | | 0 | -4 | | 0.5 | -3.25 | | 1 | -2 | | 1.5 | -0.25 | | 2 | 2 | | 2.5 | 4.25 | | 3 | 8 | | 3.5 | 12.25 | | 4 | 16 |

Step by step solution

01

Identify the given function and x-values

The given function is \(y=x^2+x-4\). We will be evaluating this function at the given x-values: $$x = -2, -1.5, -1, \ldots, 3, 3.5, 4.$$
02

Calculate y-values

For each x-value, substitute the x-value into the function's equation and compute the corresponding y-value as follows: $$ y(x) = x^2+x-4 $$ For x = -2: $$ y = (-2)^2+(-2)-4 = 4-2-4 = -2 $$ For x = -1.5: $$ y = (-1.5)^2+(-1.5)-4 = 2.25-1.5-4 = -3.25 $$ For x = -1: $$ y = (-1)^2+(-1)-4 = 1-1-4 = -4 $$ Continue this process for the remaining x-values in the given range (-0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, and 4).
03

Organize the values in a table

Now, we will organize the computed y-values with their corresponding x-values in a table: | x | y | |-------|--------| | -2 | -2 | | -1.5 | -3.25 | | -1 | -4 | | ... | ... | | 3 | y(3) | | 3.5 | y(3.5) | | 4 | y(4) | Complete the table by calculating the y-values for the remaining x-values using the same process as in Step 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

Use algebra to find the inverse of the given one-to-one function. $$f(x)=\sqrt[5]{\frac{3 x-1}{x-2}}$$

Determine the domain of the function according to the usual convention. $$f(x)=x^{2}$$

Draw the graph of a function \(f\) that satisfies the following four conditions: (i) domain \(f=[-2,4]\) (ii) range \(f=[-5,6]\) (iii) \(f(-1)=f(3)\) (iv) \(f\left(\frac{1}{2}\right)=0\)

Describe a sequence of transformations that will transform the graph of the function \(f\) into the graph of the function \(g.\) $$f(x)=\sqrt{x^{4}+x^{2}+1} ; g(x)=10-\sqrt{4 x^{4}+4 x^{2}+4}$$

In each part, compute \(g(a), g(b),\) and \(g(a b),\) and determine whether the satement " \(g(a b)=g(a) \cdot g(b)\) " is true or false for the given function. (a) \(g(x)=x^{3}\) (b) \(g(x)=5 x\) (c) \(g(x)=-2\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

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.